If you are a cleric and take a prestige class that increases the existing spell caster level, do you still gain the domain spells of the higher levels.
Example: Fire domain cleric goes to 5 then takes a prestige class for 4 levels that raises existing caster level to 9. Does he have access to Wall of Fire (4th) and Fire Shield (5th)?
My gut reaction is yes. If you are a Sorcerer taking levels in a prestige class granting levels of spellcasting in previous class (Dragon Disciple as an example), you also get new spells known. I don't see how this would be different. But as for extra domain powers (as opposed to spells), I don't know.
You still get the domain slots and domain spells if you take a cleric into a PRC that advances spellcasting. This is because you already have the domains and don't lose them when you PRC, and since the domains simply add those spell slots and spells known to your spellcasting it still goes up with the PRC if the PRC advances spellcasting.
Domain powers generally won't increase with levels other than cleric, unless the other class specifically grants such an ability.
Bonus spells not from domains generally aren't granted with a PRC. For instance, Sorcerer bloodline bonus spells are gained as a result of sorcerer levels, not spellcasting levels. These won't go up for a Sorcerer who takes a PRC unless the class specifically permits it (such as Dragon Disciple).
How can you tell the difference? Look at the advancement chart for each class. Notice how the sorcerer chart says at what levels he gets a bloodline spell? Thats tied to the sorcerer's class level, not spellcasting level. Notice how the cleric's list doesn't have 'domain spell' listed on it? Thats because its tied to spellcasting and not cleric levels.
If you are a cleric and take a prestige class that increases the existing spell caster level, do you still gain the domain spells of the higher levels.
Example: Fire domain cleric goes to 5 then takes a prestige class for 4 levels that raises existing caster level to 9. Does he have access to Wall of Fire (4th) and Fire Shield (5th)?
Yes, domain spells are part of the cleric's spellcasting. "A cleric gains one domain spell slot for each level of cleric spell she can cast, from 1st on up." p.40