Greetings, fellow traveller.
You only get the domain powers if you advance in cleric levels - the same goes for every class ability. Only if you have accumulated enough levels of that specific class you get the goodies mentioned in the class's section.
Ruyan.
In increases with your class level in the class that granted it. Unless it specifically says it stacks with levels in another class.
Unless otherwise stated, class abilities that refer to "level" are talking about class level, not character level.
It's in the section of the book about multiclassing.
Instead of gaining the abilities granted by the next level in your character's current class, he can instead gain the 1st-level abilities of a new class, adding all of those abilities to his existing ones. This is known as “multiclassing.”
For example, let's say a 5th-level fighter decides to dabble in the arcane arts, and adds one level of wizard when he advances to 6th level. Such a character would have the powers and abilities of both a 5th-level fighter and a 1st-level wizard, but would still be considered a 6th-level character. (His class levels would be 5th and 1st, but his total character level is 6th.) He keeps all of his bonus feats gained from 5 levels of fighter, but can now also cast 1st-level spells and picks an arcane school. He adds all of the hit points, base attack bonuses, and saving throw bonuses from a 1st-level wizard on top of those gained from being a 5th-level fighter.
Note that there are a number of effects and prerequisites that rely on a character's level or Hit Dice. Such effects are always based on the total number of levels or Hit Dice a character possesses, not just those from one class. The exception to this is class abilities, most of which are based on the total number of class levels that a character possesses of that particular class.