Per your question #3, the thread referenced above includes a useful link to The Guide To Sleeping In Airports | SFO. (I've retitled the link here so it's more obvious why it's pertinent.)

That page also includes references to various lounges' operating hours, which would answer your question #1.

Your question #2 was addressed above, but I'll elaborate on the answer: Yes, AA departs from Terminal 2. Your flight from HKG will arrive at the International Terminal. Per standard US airport procedure you will need to clear immigration, collect your bags, clear customs, and exit the secure zone of the airport before going anywhere else. There is no way to wait air-side in the International terminal, and there is no way to make an air-side connection to another terminal after arriving on your flight. You will be flushed out to the arrivals hall, and you will have to reenter through security-- in Terminal 2-- for your connecting flight. This will greatly limit your access to lounges.

Note also that while you plan to carry only hand luggage from HKG, any duty-free liquids carried or bought aboard the international flight will need to travel as checked luggage for your connecting domestic flight if they exceed the "3-1-1" rule.