Ideally you'd end up with 3 domain/inquisitions in a combination of your choice, but two would level with your cleric level and one with your inquisitor. If I remember correctly anyway.
Clerics cannot choose inquisitions, only Inquisitors can choose inquisitions. Having levels in Inquisitor allows you to select an inquisition, much like having levels in Cleric allows you to select domains. Of course, only levels in Cleric or Inquisitor increases the abilities of domains and inquisitions respectively.
Also, domains are restricted by alignment and/or the deity you worship, not by choosing an inquisition (unless I missed some text stating otherwise?).
Clerics cannot choose inquisitions, only Inquisitors can choose inquisitions.
Inquisitions are intended for inquisitors, not for other classes that give access to domains. While a cleric or other domain-using class can select an inquisition in place of a domain (if appropriate to the character’s deity), inquisitions do not grant domain spell slots or domain spells, and therefore are much weaker choices for those classes. These other classes use the appropriate class level as their inquisitor level for the purpose of inquisition granted powers (clerics use their cleric level as their inquisitor level, and so on).
Your information is a bit outdated. Anyone can take a subdomain or inquisition their deity/ideal qualifies for, though usually inquisitions are frontloaded and don't give bonus spells so they aren't the best pick for a cleric.
Edit: I'm a swordsage! I should add that in the case of GM fiat sometimes the best way to solve things is to ask your GM. Your GM could rule you get to scale three domains equal to you character level or you only get two that scale with your highest level class. GM Fiat is variable like that.
Clerics can take inquisitions so long as they correspond to their deity. Domains are generally more powerful than inquisitions though as inquisitions do not grant domain spells. Technically, inquisitions are not domains, therefore you are not required to take the same inquisition with your Cleric levels. However, most GMs would probably rule that an inquisition is similar enough to a domain that you must follow the domain rules for it and pick it as one of your Cleric domains. Since inquisitions were released in Ultimate Magic and not the Advanced Player's Guide, I would probably take this stance in a home game. In PFS, the technicality should work for you.