What is the minimum connection time needed at TPE? We have a flight from LAX-TPE that arrives at 6:25AM on Malaysia Airlines. I want to book a separate flight from TPE-BKK. Does an 8:30AM EVA Air flight give us enough time? I am assuming that we will need to retrieve our luggage and recheck them in through EVA Air. Also, I believe that Malaysia Air is in Term 1 and EVA Air is in Term 2.

I would give it more time than that. You will need to collect your luggage, and I assume go through some sort of immigration/transit procedure, then check in on time for the next flight. Your ticket purchased seperately, unless you buy a full fare with no restrictions, will not be easily changed in the event you miss the flight due to a delay on your previous flight or holdup at baggage or something.

A good alternative would be to book your itinerary as one ticket, in which case you would have protection for the second flight if you miss it because of trouble on the first flight. It also might be possible to check in for all of your flights in LAX if the airlines interline.

About a very similar question:
http://flyertalk.com/forum/showthread.php?p=7625439