The warlock's ability to regulate (to some degree) the effects of her eldritch blast (like damage) by lowering the blast's effective caster level has no impact on her ability to pick or employ metamagic-like feats related to the eldritch blast.
The eldritch blast's spell level
The warlock's effective caster level of her eldritch blast isn't the same as the eldritch blast's effective spell level. (This overuse of the word level dates to the game's inception, even inspiring a favorite Web comic strip.) The spell level of eldritch blast was changed by the Complete Arcane errata:
Page 7: Eldritch Blast
Second paragraph of the Eldritch Blast ability description: Change “An eldritch blast is the equivalent of a spell whose level is equal to one-half the warlock’s class level (round down), with a minimum spell level of 1st and a maximum of 9th when the warlock reaches 18th level or higher” to “An eldritch blast is the equivalent of a 1st-level spell. If you apply a blast shape or eldritch essence invocation to your eldritch blast (see page 130), your eldritch blast uses the level equivalent of the shape or essence.”
Any other references to eldritch blast being something other than the equivalent of a 1st-level spell should be disregarded. Any other references claiming that eldritch blast is not an invocation should be disregarded. A warlock can use eldritch blast at will. (1)
This means for most purposes except as pointed out by the errata the eldritch blast is effectively a 1st-level spell. Thus, for example, a warlock must possess at least a caster level of 6 (therefore usually being a level 6 warlock) to take the feats Empower Spell-like Ability (eldritch blast) (Monster Manual 303) and Maximize Spell-like Ability (eldritch blast) (Complete Arcane 81), and a warlock must possess at least a caster level of 10 (therefore usually being a level 10 warlock) to take the feat Quicken Spell-like Ability (eldritch blast) (Monster Manual 304).
The eldritch blast's caster level
Because, except for a few situations (like, for example, its lack of components), "a spell-like ability functions just like a spell" (PH 180), this means an eldritch blast can be employed "at a lower caster level than normal, but the caster level you choose must be high enough for you to cast the spell [i.e. employ the blast]…, and all level-dependent features must be based on the same caster level" (PH 171). Thus, a level 7 warlock could opt to employ the eldritch blast as if her effective caster level were, instead, 6, 5, 4, 3, 2, or 1.
For example, to bring this all together, if she wanted to for some reason, a level 7 warlock that possesses the feat Empower Spell-like Ability (eldritch blast) can use the feat yet employ the blast as though her effective caster level were as low as 1.
It’s unclear, unfortunately, whether the “selection” is a thing done once, when you take Quicken Spell-like Ability, or if you must constantly re-select the same choice every time you want to use it—that is, whether or not you have to re-check the spell-like ability’s spell level each time.
If you don’t, then as long as you had CL 10th when you selected eldritch blast (which is necessary to meet the feat requirements anyway), you could select eldritch blast as the spell-like ability in question, and then no matter what changes happen later, you could use quicken eldritch blast.
On the other hand, if the selection is something you have to do again each time you use Quicken Spell-like Ability, then you have an issue. A brimstone blast may still “be” eldritch blast for the purposes of being the spell-like ability you chose originally, but brimstone blast does change the spell level of that spell-like ability to 3rd. Until CL 14th, Quicken Spell-like Ability would not allow you to select a 3rd-level spell-like ability. Therefore, you would have to wait until CL 14th to use it on a brimstone blast.
I feel that the rules text favors the former interpretation, of selecting just once when the feat is taken, but the rules text was also definitely not written with consideration for spell-like abilities that change spell level. That’s not something that spell-like abilities do—except for eldritch blast.
Best Answer
I love the factotum, but it is notorious for its poor editing. This is just another example. Note that Dungeonscape never received errata. Frankly, the fact that the class was written by Jason Bulmahn, who later created Pathfinder, which is equally-notorious for its failure to correct mistakes, seems telling.
The Sp almost-certainly refers to the fact that arcane dilettante gives you spell-like abilities, not that it is itself a spell-like ability. The process of preparing arcane dilettante SLAs, itself, makes little-to-no sense as a spell-like ability, and frankly leaves us no good answer to questions like yours (though I’ll try, below). This is out of keeping with the standard practice in 3.5e, where abilities that give you a set of abilities are untyped—contrast the “Invocations:” on Complete Arcane page 7, which is a feature that allows you to pick out some SLAs but isn’t, itself, marked with “(Sp).” On the same page, we have “Eldritch Blast (Sp):” which is, because eldritch blast is the name of the SLA itself.
So arcane dilettante shouldn’t have the Sp. Or, if it does, it should, supposedly, mean the actual preparation process described in the arcane dilettante feature is itself spell-like, and that doesn’t make any sense, so this is a “proof” (ish) by contradiction. That makes your questions fairly easy to answer:
No, because arcane dilettante isn’t, itself, a spell-like ability; it just lets you prepare things that are spell-like abilities. No interaction.
I’m not actually sure what this means, but taking a feat is hardly “free” here, so no? If this is stemming off of assuming a “yes” to the previous bullet point, then also no.
Yes. Arcane dilettante explicitly says that the spells prepared through it are cast as spell-like abilities—that means the meta-spell-like feats apply to them.
Trying to puzzle out RAW: can’t just ignore the Sp tag
OK, all that is well and good, but ultimately, Dungeonscape has the “Sp” tag on this ability—at least from a RAW perspective, we can’t just ignore that, even though we probably should. What, then, does it mean?
We’ll start with precedent. There is one other possible RAW case for an ability that lets you pick out other abilities being, itself, an ability of a certain type: “The manifestation of powers by a psionic character is considered a psi-like ability,” Expanded Psionics Handbook page 65. As I’ve discussed elsewhere, no one really knows what that means, either. Most likely, it just means that when you manifest a psionic power, it counts as using a psi-like ability and triggers any “when you use a psi-like ability” rules. It’s not even clear whether “the manifestation” here means the fact that you have powers at all is, itself, a psi-like ability (and it’s utterly unclear what that would mean), or if each individual “manifestation” (read: “casting” equivalent) is psi-like (which is still a bit unclear). So this is our only precedent, and it does not help.
Leaving that aside, if we are to treat arcane dilettante itself as a spell-like ability, the first thing we need to know is its spell level. Every spell-like ability has to have a spell level; it’s part of the saving throw DC calculation, and it interacts with tons of things that SLAs might interact with, such as the meta-SLA feats you note. Arcane dilettante doesn’t mimic any actual spell—which most SLAs do but the rules for SLAs do explicitly note the possibility for SLAs to not do that—so we expect the rules for arcane dilettante to define its spell level. Those rules do not.
This does sort of lead us to an answer to the question of how arcane dilettante interacts with meta-SLA feats: when the feat asks “does this SLA have a spell level below X?” then for arcane dilettante we basically have to answer “we don’t know that it does,” and since the feat requires us to answer with “yes,” we can’t use the feat.
But not all such feats actually concern themselves with spell level. So what about those? Well, first of all, unless the feat specifically says something to indicate it, there’s no reason to assume that the effects of the feat are transferred to all the spells you prepare—you would need to use the feat on those spells individually. Using the feat on arcane dilettante itself only affects the use of arcane dilettante itself, not the SLAs you get as a result.
Boost Spell-like Ability (Book of Vile Darkness)—Preparing spells with arcane dilettante doesn’t trigger any saving throws, so boosting its undefined DC doesn’t matter.
Consecrate Spell-like Ability (Book of Exalted Deeds)—the act of preparing your arcane dilettante SLAs is now has the [Good] descriptor. That probably makes it a good act (though ask your DM because that’s never actually defined). It doesn’t seem to have any other effect that I can think of, unless you have some other ability that triggers when you cast something with the [Good] descriptor or something.
Corrupt Spell-like Ability (Book of Vile Darkness)—evil counterpart to Consecrate, see above.
Purify Spell-like Ability (Book of Exalted Deeds)—basically the same as Consecrate, except it also makes the spell do no damage to good creatures, less damage to neutral creatures, and extra damage to evil creatures. Arcane dilettante doesn’t deal damage, so that’s irrelevant; see the above discussion of Consecrate for details on the [Good] aspect.
Spell-like Ability Focus (Races of Faerûn)—identical to Boost Spell-like Ability; see above.
Spell Stowaway (Tome and Blood)—this epic feat lets you “gain the magic’s effect” when someone else uses the spell-like ability you chose with this feat. So if you chose arcane dilettante, and someone else used arcane dilettante, “you also immediately gain the magic's effect as if it had been used on you by the same caster.” That is pretty awesome, as the effect of arcane dilettante is getting several additional SLAs. You would still have to use your own inspiration points to cast them, and could only use each once, but it’s still a substantial expansion of your capacity. But since it requires 24 ranks in Spellcraft, I don’t particularly care.
Supernatural Transformation (Savage Species)—no spell level concerns, but arcane dilettante isn’t “innate” for any creature, so no one can use this feat on it.
Violate Spell-like Ability (Book of Vile Darkness)—like Corrupt, but it also changes the SLA to deal vile damage. Arcane dilettante doesn’t do any damage, so that doesn’t matter. So this ends up being the same as Corrupt, which means see the discussion of Consecrate and switch the descriptors around.
And those are all the feats I could find that might have an interaction—the only meaningful one is Spell Stowaway, and that’s epic, and even then it only matters if you have another factotum to use it with.