Answer to Question 1
Domain levels from your base class and Exalted prestige class do not stack, unfortunately. There are prestige classes that do stack with existing domain levels (Hellknight Signifer, Stargazer, and Dawnflower Anchorite, for instance), but Exalted, for whatever reason, does not. I'd say that Exalted's domain powers would at most be capped at 10th level but if you are particularly strange you can advance the Exalted prestige class with the Evangelist prestige class and obtain both sets of boons. So if you choose to follow 5 levels of Exalted with 10 levels of Evangelist, you would have 14 levels of Exalted. The last 4 levels of advancing as if you took extra levels in Exalted would do nothing except scale up any class features that scale with Exalted level. This is not particularly worthwhile, especially since you lose a level of advancement thanks to Evangelist, but since we are discussing the upper maximum, I would suspect 14 levels of domain powers from Exalted to be that upper limit, assuming no epic levels.
Answer to Question 2
Correct. Regardless of advancement of domain powers, your access to domain spells scales with your caster level and spell slot. If a Cleric were to enter the Veiled Illusionist prestige class, for instance, he would still obtain access to all his domain spells as he continues advancing spellcasting despite not advancing any of his domain powers. So you would have full access to all 3 domains' spell lists at full caster level for your domain slots. This is also sometimes used as a way for Druids with a domain bond to add a Cleric domain. 6 levels of Druid followed by Exalted with a single Shaping Focus feat gives the Druid sufficient advancement of wild shape for most purposes.
Answer to Question 3
The text "The exalted can use each spell-like ability only if she is able to cast divine spells of that level." uses your spellcasting to determine access to SLAs, meaning that if you can cast a spell of that level, you obtain access to the domain SLA of that level. So if you can cast 9th level spells, you gain all 9 domain spells as a spell-like ability once per day. If you have 6 levels of Druid and 5 levels of Exalted, then you can cast spells of the 6th level, so every domain spell from your Exalted domain from spell levels 1 to 6 is gained as a spell-like ability, and as you continue advancing spellcasting and unlocking higher level spells, you gain access to higher level spell-like abilities.
Just to be clear, spell-like abilities do not have caster level requirements to be usable. An Aasimar can use Daylight as a spell-like ability at level 1 with a caster level of 1, for instance, despite that being a 3rd-level spell, so the caster level of the Exalted spell-like abilities has no bearing on when you unlock them.
