Core Bestiary
They can cross over (by flight, bridge, or being carried) running water, but not pass THROUGH the water (swimming, etc) lest they risk permanent destruction, as their mist form escape doesn't function when they are slain by running water.
Pathfinder Splats
Classic Horrors Revisited very briefly mentions them being thwarted by running water, but doesn't specify they can't cross it, so I'm assuming that's a reference to the damage they take if immersed. It also very specifically says that many vampires don't adhere to the generic vampire rules, as I point out below, and relying on a single "traditional" weakness could be an adventurer's last mistake.
At the table
While your question asks for RAW, with all our talk of vampires (now spanning three questions), I feel I should mention that vampires are one of the most, if not the most, house-ruled monsters there are. Adding and subtracting classic weaknesses, separating them into clans (along lines such as games like TES4:Oblivion or Vampire: the Masquerade), or simply giving them class levels you might not expect (It's a vampire... cleric of a neutral deity? Channeling negative, oh dear...); all of these and more are ways vampires quickly find themselves telling RAW to bite them (pardon the terrible pun). If your vampire friend finds himself stymied by running water, great; beware your DM didn't remove a different classic weakness to add that one. If the vampire is in full-plate, don't assume that means he can't cast fireball; the Tremere clan's blood magic cares not for your arcane-spell-failure rules.
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.
Best Answer
What Jeremy Crawford, Unofficially Says
Jeremy Crawford answered the question of what is running water. To the question:
Jeremy answered:
He then clarified, when asked about water elementals:
http://www.sageadvice.eu/2016/04/26/vampire-in-running-water/
How it applies
So, based on that, If you can get enough water out of the decanter that it is stream or river like for your DM, then you're good. But even with the clarifications it is a DM call. I personally think 1 foot x 1 foot of moving water is enough to count as a body of running water.
I, personally, would give the vamp a dex save (DC 15??) to see if he can dodge it before it hits him.