My research, and Hero Lab tell me 1) one and 2) no, which is not the answer I was looking for. On the other hand, when you stack a bunch of domain eligible classes and archetypes within Hero Lab the results seem, unreliable.
Which brings about question 3.
3) When a Cleric has two Archetypes that both allow only a single domain, does the Cleric get one domain or zero? Hero Builder seems to think zero, unless I'm doing something wrong with my Cloistered Cleric/Divine Strategist. It doesn't seem right that a two Archetype Cleric should get zero Domains.