Type

Every creature must have a type, and there is a strict, limited list of types:

• Aberration
• Animal
• Construct
• Dragon
• Elemental
• Fey
• Giant
• Humanoid
• Magical Beast
• Monstrous Humanoid
• Ooze
• Outsider
• Plant
• Undead
• Vermin

Types have shared rules and abilities (for instance, all undead have Con —, all Outsiders have difficulty being raised from the dead, all Animals have Int 1 or Int 2, etc.), and most importantly, definitions for Racial Hit Dice (all Dragons have d12 HD, good BAB, all good saves, and 6+Int skills, all Giants have d8 HD, medium BAB, good Fortitude, and 2+Int skills, etc.).

Note that these statistics affect only racial hit dice (innate hit dice), not hit dice from class levels (e.g. a white dragon wyrmling sorcerer 2 has five total HD: 3 racial HD, which use d12s, good BAB, all good saves, and 6+Int skills, and 2 sorcerer HD, which use d4s, poor BAB, good Will only, and 2+Int skills).

Types are often refered to in spell targeting restrictions (e.g. charm person’s “One humanoid creature” means a single creature of the Humanoid type) or in the requirements for feats (e.g. Rapidstrike), prestige classes (e.g. Dragon Disciple), or templates (e.g. Celestial).

Subtype

Subtypes can be almost anything. The only thing all subtypes have in common is that they group together all the creatures who have that subtype.

Despite the name, subtypes are not always “within” a type; several subtypes can be found across many types (the Fire and Cold subtypes, in particular, are extremely common and can be found on literally any type of creature).

Unlike types, for which there is a very specific, limited list, subtypes can be created on a whim, and sometimes are used very narrowly (e.g. the marruspawn subtype was applied to four creatures from a single book, and never used elsewhere). Other times (such as the elemental or alignment subtypes), they’re used very broadly, on many many creatures across several different types.

Some subtypes have rules shared by all creatures who have it (e.g. all creatures with the Fire subtype are immune to fire damage but vulnerable to cold damage), while other subtypes have no significance at all beyond marking creatures as members of a group (e.g. there are not any specific things that all creatures with the Elf subtype share, aside from the fact that they have the Elf subtype).

Subtypes can be permanent, intrinsic parts of a creature, or they can be temporary, added or removed on a whim. Some subtypes can be intrinsic for one creature, while temporary for another (e.g. a thoqqua will always have its Fire subtype, while a barbarian with the Blazing Berserker feat will gain and lose the Fire subtype several times a day).

Some subtypes are even automatically gained by any creature who meets certain requirements: if you have at least 1 power point, then you have the psionic subtype. If you have at least one 1 point of essentia, then you have the incarnum subtype. These subtypes literally just exist as a simple way of categorizing certain groups of creatures: “any psionic creature” is shorter and easier to write than “any creature with at least 1 power point.”

Which is ultimately the point of subtypes: to be able to easily, within the rules, refer to all creatures with the subtype. Sometimes they put shared rules all in one spot, but other times they don’t even do that: The Elf subtype exists so that authors can be sure they get all elven sub-races; that is its only purpose.

Race

This just is; almost nothing changes it. The reincarnate spell and spells that mimic it are the only examples that I can think of. Most things that refer to a race by name really mean the race’s subtype, so something that requires the “Elf race” works for all elf sub-races, as all give the Elf subtype. As such, one’s race has little weight beyond the actual racial features it offers (but one of those features will be a possibly-relevant subtype).

Templates

Templates change a creature. That is their function.

A template may change type or subtype; this is not required (or even all that common; especially in later books, tons of templates were written for turning undead creatures into scarier undead creatures). A template may work only on members of a particular type, or even members of a particular subtype, or they may work on anything at all, or have other requirements like “living” or “corporeal.”

A template provides a unified series of adjustments that you can make to any (qualifying) creature to make systematic changes. For DMs, they offer ways of modifying and upgrading monsters beyond mere HD; for players they can offer different ways of customizing a character.

In a lot of ways, subtypes and templates can serve similar functions: they consolidate a set of rules that can be applied to numerous creatures, without rewriting them. The big difference is that subtypes are applied to creatures when they’re written, or through specific means – the game does not expect anyone (even the DM) to slap a subtype on any given creature. That is what templates are for: modifying a creature. Even if the modification is just to add a subtype. This distinction is important, because templates come with a sense of value or cost: templates apply adjustments to a creature’s Challenge Rating or Effective Character Level, indicating that they are more powerful with the template than they would be without it (and, in theory anyway, how much more powerful). Subtypes do not come with any indication of their relative value.

Specific Examples

Human with Mark of Passage

Yes, the race would be Human, but this doesn’t matter very much. This was very unclear originally, but was clarified in Races of Destiny – the “human race” requirement actually cares about the subtype. Which, yes, is (Human), with the Humanoid type.

Elf Vampire

The elf’s race is still Elven, and the type changes (per the template) to Undead (Augmented Humanoid). The overwhelming majority of templates that change type indicate that the creature should retain any subtypes it had, which Vampire neglects to do. I’d chalk this up to oversight in an early book, personally: I’d suggest that the vampire would be Undead (Augmented Humanoid, Elf).

The dragonmark is more interesting here; the Vampire certainly doesn’t change race, and as I mentioned, I’d argue it shouldn’t change subtype, either. But it should prevent the use of the dragonmark: it is a major plot point in Eberron that Erandis d’Vol lost the ability to use her Mark of Death when she became a lich. The same thing should happen to a vampire, but the Least Dragonmark et al. do not mention it. I’d treat this as an oversight and modify the requirement to be a “Living member of appropriate dragonmarked race and house.”

Radiant creature

Radiant creatures retain their race, yes. Again, as with the Vampire, I’d argue that they keep subtypes, as well. Moreover,

Native Subtype

A subtype applied only to outsiders. These creatures have mortal ancestors or a strong connection to the Material Plane and can be raised, reincarnated, or resurrected just as other living creatures can be. Creatures with this subtype are native to the Material Plane (hence the subtype’s name). Unlike true outsiders, native outsiders need to eat and sleep.

The native subtype is a pretty solid thing to have.

The rest

None of these change race; again, basically nothing does. I’d argue that, outside of explicit changes to subtype (explicitly adding or removing named subtypes), templates should not change subtype, as it confuses things (and later on it became common for Wizards to specify that templates didn’t, but only in individual templates). Sometimes this does get a little screwy – for example, the Dragonborn template explicitly retains subtypes, which is weird for the Living Construct subtype, as you get a Humanoid (Dragonblood, Augmented Construct, Living Construct) creature. But not doing it is truly bizarre in cases where the addition of subtypes should be permanent – someone with the Dragontouched feat should retain the Dragonblood subtype even if they later become Undead. And certainly all the human subraces should retain their Human subtype, all the elven races should retain their Elf subtype, and so on.

It doesn't say it counts as armor or natural armor or anything, so it doesn't. It's just 1 AC on top of everything else, to emphasize the sturdiness of Warforged. It should stack with everything and prohibit nothing.

To support this, note that the Warforged trait provides a bonus to AC, rather than setting it to a number, as armor is wont to do. The Tortle, another race with an armor-related ability, sets its armor class to 17 like armor usually does, and correspondingly disallows further benefits from wearing armor, further illustrating that abilities that provide bonuses to the class of worn armor (like the Warforged trait) are not armor and are intended to modify armor, while abilities that provide a different default armor class probably count as armor and definitely don't modify the effective class of worn armor.