Can the “Anyspell” spell be used effectively by a spontaneous divine caster with the Spell Domain

The two terms are not synonymous, but from a rules perspective, they are very near it. At least a few rules citations - some from your examples, and a few more I've cited below - indicates that "casting spells without preparation" qualifies as "casting spells spontaneously", but casting spontaneously isn't the same as casting spells without preparing them.

First, to clear up the part I feel is most importent: Sorcerer and bard spellcasting is "spontaneous" for the purposes of feats like in your examples. Please see the Quicken Spell feat description on page 98 of the Player's Handbook:

Special: This feat can’t be applied to any spell cast spontaneously (including sorcerer spells, bard spells, and cleric or druid spells cast spontaneously)

While the only mention of "spontaneous" in the actual Sorcerer's entry is in a lore section regarding how they start learning magic, it's pretty clear that the rules were written where "casting a spell you haven't prepared" qualifies as "casting a spell spontaneously". Other mentions include:

• The introduction to magic, page 169
• The introduction to the bard, page 26.

This section contains speculation: It's weak, but it's there. I find it very likely that when 3.0 was first being developed, they didn't have a name for it yet (and wrote up the sorcerer's class entry before coming up with a name for their casting style) - and then that wording stuck, especially to the feats and definitions when they were ported to 3.5 with little context. I find it especially telling that while Quicken Spell definitely refers to sorcerer casting as spontaneous, the glossary specifies that spontaneous casting is a cleric and druid ability. It's a recurring problem in OGL d20 games, as there is a LOT of copy-pasta to swallow - the language evolved, but the text did not, even when "updated".

I will try to get some more detail when I can get my hands on a 3.0 corebook, but as far as 3.5 is concerned: The wording has been spotty, but at least one rules reference starting with the core PHB has always suggested that a sorcerer or bard's spellcasting has always been considered spontaneous.

However, it should be noted that the terms are not transparent in the other direction. Clerics and druids do not cast spells without preparation; they must have prepared spells in order to have spells to sacrifice to power their spontaneous casting of three letter abbreviations. While this primarily only affects corner cases, this does mean the terms are not synonymous. For example, a wizard who has taken the Elemental Adept feat (and thus is capable of casting spontaneously) still doesn't qualify for the Air Bloodline feat, which requires the ability to cast without preparation.

So to conclude, while the terms can be used interchangeably to refer to sorcerer and bard spellcasting, there is a divide when referring to divine casters (as well as casters like wizards who've taken the Elemental Adept feat) that can matter in some cases. It is probably best to think of "casting without preparation" as a subset of "casting spontaneously": if you can cast a spell using a slot you didn't prepare that spell in, whether or not you prepared any spell in that slot, then you can cast spontaneously; but you have to be able to cast a spell using a slot you didn't prepare any spell in to be able to cast without preparation. So no, the terms are not synonymous, although sorcerer spellcasting is spontaneous. Casting without preparation is always casting spontaneously, but there are many cases in which casting spontaneously is not casting without preparation.

Touch of Healing: Definitely Yes

Getting the easy part out of the way first. If you can spontaneously cast a Conjuration (Healing) spell, and have a spell slot available in which to do so, you have it “available” as required by Touch of Healing. The fact that you have something else currently prepared in that slot doesn’t matter in the least when you can ditch that whenever you want.

Otherwise, Touch of Healing would fail entirely for favored souls, and I don’t think anyone wants to make that case.

Empowered/Maximized Healing

RAW, probably Yes

Unfortunately, the rules not only fail to delineate exactly what a “domain spell” is or is not, but also use that phrase to refer to two related, but subtly different, things.

That is, we have that

Each domain gives the cleric access to a domain spell at each spell level he can cast, from 1st on up...

If a domain spell is not on the cleric spell list, a cleric can prepare it only in his domain spell slot.

where “domain spell” is used to refer to each of the spells on your domain lists, as unprepared, almost abstract concepts—potential spells you have the option of preparing and casting, but before we get to those steps. Tellingly, it says “Each domain” has—or, more accurately, “grants access to,”—a domain spell per spell level—that is important because most clerics have more than one domain, so we are talking about more than one domain spell per spell level. The latter quote here clearly indicates that “domain spell” as a phrase can refer to any of the spells on domain lists, even if they aren’t yet prepared—because it specifies where you can prepare them, which is meaningless if you’ve already done so.

Contrast that with

A cleric also gets one domain spell of each spell level he can cast, starting at 1st level.

Here we’re taking about a real, tangible thing, a prepared spell, that the cleric could cast, or, say, a spellthief could steal. And you only get one of this kind of “domain spell” per spell level per day, unlike the other meaning of that phrase where you got (access to) one for “Each domain,” and there is no “per day” involved because your access to them is permanent and constant. This one domain spell per day is the result of taking the access to domain spells provided by our domain, and preparing them in our domain slot:

When a cleric prepares a spell in a domain spell slot, it must come from one of his two domains (see Deities, Domains, and Domain Spells, below).

(For context, this sentence immediately follows the previous quote. Note that the “Deities, Domains, and Domain Spells” section referenced here is the source of the first two quotations in this answer.)

So we have two subtly-different meanings of the term “domain spell” here—one refers to any and all spells found on domains, and the other refers to the one spell per level per day you can prepare in your domain slot and cast, and both are just “domain spell.” Herein lies our real problem—which of these two meanings of the phrase is radiant servant of Pelor using? Radiant servant of Pelor, itself, doesn’t really give us a lot to go on either way.

However, there is a context that is very important: the one place where “domain spell” is definitively used to refer to the actual prepared-and-cast spell is in a paragraph that is all about discussing how many spells of each level a cleric can cast per day. That is, what they’re discussing here actually is your one “domain spell” per day of each level. In this sense, a “spell per day” is different from a “spell,” in that your “spells per day” (for each spell level) is the number that your domain spells ability adds +1 to, while the “spell” is the actual, ya know, spell, found on the domain list.

Also, importantly, that one time “domain spell” is used to refer to that one spell per day per level is in the spells section—and immediately refers you to the “Deities, Domains, and Domain Spells” section for more details. The section that includes “Domain Spells” in the title, and to which everything else directs you for information about domain spells, uses the term solely to refer to the spells on your domains’ lists, and not your one extra spell per day per spell level that is prepared in your domain slot.

Therefore, it seems to me, that the most likely definition for “domain spell” is “a spell found on your domains,” and not (necessarily and solely) “a spell prepared in your domain slot.” The use of that phrase in the cleric’s spells ability is actually (in context) the result of eliding the “per day” that was already under discussion, and which is indeed limited to one per spell level that corresponds to whatever you decide to put into your domain slot for each level. It is therefore very likely that “properly speaking,” RAW, the radiant servant of Pelor is referring to any spell of the Healing domain list, regardless of how it is cast.

But a strong circumstantial for No being the intent

But we should go back to the radiant servant of Pelor at this point, because while it doesn’t give us a lot to go on, there may be something:

When a radiant servant of Pelor of at least 2nd [6th] level casts a domain spell from the Healing domain, that spell is affected as though by the Empower [Maximize] Spell feat. This spell does not use up a higher-level slot.

If we understand “domain spell” to refer to those spells you got access to because of the domains you have, the use of that phrase here would be entirely redundant with “spell from the Healing domain,” since of course (near-tautologically) a spell from the Healing domain is a spell from a domain. Furthermore, radiant servant of Pelor here is emphasizing that you cast the domain spell, which isn’t quite something you can do with a spell on a list—you have to prepare it in a slot, and then it is the prepared spell that you cast. This is a lot closer to what the spells section is talking about when it says “A cleric also gets one domain spell of each spell level he can cast,” since that prepared spell is the physical manifestation of that extra spell per day (per spell level) that the cleric gets. That makes for a strong, if circumstantial, case for thinking that the authors of radiant servant of Pelor may not have been as careful about this as we may have liked, and were referring specifically to the one prepared in your domain slot.

On top of this, spontaneous domain casting itself even states you cannot use “a domain spell” to spontaneously cast another spell from your chosen domain. again, that only makes sense if they’re talking about the spell prepared in your domain slot—otherwise any spell available from one of your domains, or maybe even from any domain, would be ineligible for being spontaneously converted to one of the spells from your chosen domain, and that certainly doesn’t seem likely at all.

How things work out in each case:

If a “domain spell” is any spell you get access to from a domain, as RAW seems to indicate, then you can use spontaneous domain casting to cast it and it’s still a domain spell, but then at that point you could have just prepared it to begin with (or, in the case of most Healing domain spells, spontaneously cast them using the core cleric spontaneous casting feature).

If a domain spell is specifically the spell prepared in the domain slot—which, again, it probably isn’t RAW, but there’s evidence here that both the authors of radiant servant of Pelor and spontaneous domain casting itself thought it was—then spontaneous domain casting doesn’t really help. Nothing in the ACF specifies that the process of spontaneously casting one of these spells with the ACF made it into a domain spell.

On balance: I’d allow it

It seems pretty clear to me that the authors were not clear on what exactly “domain spell” as a term should refer to. Furthermore, radiant servant of Pelor is a pretty garbage prestige class, and the empowered and maximized healing features are extremely poor. At the end of the day, the real answer is the one that makes for the best game, and that at least is quite clear: cure spells need all the help they can get, and someone dedicating themselves to those spells does likewise. Frankly, I’d nix all mention of “domain spell” from radiant servant of Pelor and allow those features to apply to any of the spells from the Healing domain, regardless of how or when you cast them. So you shouldn’t even need the spontaneous domain casting ACF for it (though you may want it since a few of those spells are superior to the cure spell you’d otherwise be able to cast spontaneously).