Yes.
The template lists all weaknesses of Vampires:
Weaknesses: Vampires cannot tolerate the strong odor of garlic and will not enter an area laced with it. Similarly, they recoil from mirrors or strongly presented holy symbols. These things don't harm the vampire—they merely keep it at bay. A recoiling vampire must stay at least 5 feet away from the mirror or holy symbol and cannot touch or make melee attacks against that creature. Holding a vampire at bay takes a standard action. After 1 round, a vampire can overcome its revulsion of the object and function normally each round it makes a DC 25 Will save.
Vampires cannot enter a private home or dwelling unless invited in by someone with the authority to do so.
[...] (exposure) to direct sunlight, [...] immersion in running water, [...] wooden stake through [the] heart [...]
Assuming your temple is not laced with garlic and is not a private home (or inside a private home), the most troublesome part are holy symbols.
Seeing that it takes a standard action to repel a vampire using a holy symbol, "strongly presented" seems to refer solely to characters or NPCs "strongly presenting" their holy symbol, as in the description of Channel Energy:
A cleric must be able to present her holy symbol to use this ability.
Arguably though, holy symbols in a temple are "strongly presented", they are usually central to the whole design (think of crosses in christian churches).
(Personally, I'd rule the latter case, because I don't like the idea of vampires walking in the front door of a Sarenrae temple, but commoner with a carved holy symbol can repel him...)
In any case, the weakness does not pertain to unholy symbols, so your bad guy is good to go.
Typical area spells found in evil temples of doom also don't hinder vampires. In fact, a vampire benefits from desecrate the same way all undead do. Unhallow also has no special effect that prevents a vampire from entering. As Jeor Mattan points out, not even hallow can prevent Vampires from walking in the front door.
The step from Spawn to Vampire is described on page 295 of the Monster Manual as:
If a true vampire allows a spawn to draw blood from its own body, the spawn transforms into a true vampire no longer under its master's control.
Interestingly enough, that suggests that any true Vampire can promote a Spawn, not just the Vampire that created the Spawn.
Best Answer
Easy bit first ...
The vampire can't - other people or circumstances can force a vampire inside. This is allowed because it is not the vampire that is doing it.
Further, once in, there is no obligation on the vampire to leave but if it does it cannot voluntarily re-enter without an invitation.
Now for the tricky bit ...
Vampires are not barred from entering non-residences like shops, warehouses, taverns and inns (but private rooms in an inn may be a residence). Given that the occupant described is specifically the occupant of a residence it seems reasonable to restrict the definition to those people who are (or are legitimately acting on behalf of) a resident of the particular residence concerned.
If the character owns or leases the house then they can issue the invitation. Similarly, if they are a guest of the resident they should be able to issue the invitation. However, if they themselves are breaking and entering then they cannot issue the invitation.
Saying "come in" is an invitation. Sending a gilt-embossed party invitation is an invitation.
Grabbing someone by the ear and dragging them inside is also a (very rude) invitation. Indeed, it is an invitation that won't take no for an answer.