1/ By definition, award ticket does not earn miles.
2/ I believe you mean CX - Cathay Pacific symbol is CX. Most of its discounted fares even are higher than its regional competitors, DONT earn AA miles. You need to read the program rules to understand the details.
3/ You may be better off to keep both AsiaMiles and AAdvantage accounts.
4/ Again, study program rules - elite status of most all airlines are from ACTUAL flying, and one has to re-qualify EACH YEAR - meaning Each Year you start from ground 0 in terms of earning the elite status. Only AA uses miles from ALL sources to count for Lifetime elite status - which is an UNPUBLISHED benefit - 1 Million cumulated miles earns you Lifetime Gold (the lowest elite tier of AA), 2 Million earns you Lifetime Platinum (the mid tier). Executive Platinum must be earned via B(utt) I(n) S(eat) miles and re-qualify each year.
5/ Regarding hotel programs - keep in mind, most hotel chains only credit stays and thus let you earn hotel points when bookings are made directly with the hotel chain itself. That often translates to a much higher rate than when you book thru discounted, 3rd party bookings.
Again, you would be much better off to study program details to see if you can meet the rules of programs then to make an educated decision.