1. There is a lot of discussion on the (poor) lounge facilities at LAX here:
http://www.flyertalk.com/forum/showthread.php?t=430657
2. I believe that AA will check your luggage through from the originating airport and also provide your boarding cards there. You should be able to proceed straight through security at TBIT; if the queues are long then you may need to go to the CX desk to get an escort to take you through the "fast lane".
3. 30 minutes. If you are in the CX lounge then they will call the flight for boarding.
4. The Chinese tea is on the menu - there is only one menu, not one for Americans and one for the rest of us The best tip is to chat to the cabin crew, tell them it's your first time and see what they suggest.
5. There are no arrivals lounges at HKG. Depending on what hotel you are staying at they may have a health club where they would be happy for you to have a shower when you arrive and drop off your luggage.
PS. This is much discussed in the Hong Kong forum.
http://www.flyertalk.com/forum/showthread.php?t=423380
http://www.flyertalk.com/forum/showthread.php?t=397776
http://www.flyertalk.com/forum/showthread.php?t=328725