What airline/airline alliance for frequent travel between KTM and various airports in the US [closed]

Would it be more beneficial to park all of my points in QA or AA?

Unless you are earning a lot of points, it is usually better to put your points in one basket, particularly in the same alliance. Which one is better for you is a matter of personal circumstance. Consider also FlyerTalk's guide. As a rule of thumb, airlines treat their own elites best, so if you do most of your flying on AA, better to be an AAdvantage member than a Qatar Privilege club member. Naturally, there are exceptions.

Since I'm a US resident, the benefit of AA is that I could get their credit card to accrue more miles

This is a useful benefit, particularly if you are able to put your own travel expenses on the card and claim them back later.

I don't think I can get the QA credit card as I'm not a resident of Qatar

Qatar Airways may have partnerships with American banks, although I did not see any on their webpage.

I imagine that I'll be doing more flying with QA than AA

AA has a sour relationship with Qatar Airways, which always has the possibility of deteriorating further and affecting earn/burn rates between the two airlines.

AA does have a partnership with Etihad, including a codeshare on Middle Eastern flights. AAdvantage members can earn points and miles on EY-coded Etihad flights even though Etihad is not in oneworld. To my knowledge, no other oneworld programme offers this. I would look carefully at this option.

Based on what I've been able to figure out, I can't directly get status with AA credit card.

That is correct.

Are miles that I accrue with my card status earning?

Note that the AAdvantage programme now has a concept of Elite Qualifying Miles, Elite Qualifying Segments, and Elite Qualifying Dollars. You need to earn the miles, plus the appropriate number of either EQSes or EQDs.

Miles you earn through spend with the cards are not elite-qualifying, but on some cards after you pass a certain annual spend threshold (either $20,000 or $40,000 depending on the card) you receive a large lump sum of Elite Qualifying Miles. Similarly you can obtain Elite Qualifying Dollars in a lump sum at a spend threshold, but mostly EQDs are earned through spending directly on AA tickets. You also earn EQDs in a different way when you buy qualifying flights on non-AA ticket stock. This is complicated. See also FlyerTalk's guide on EQDs.

Do other perks of the credit card transfer to when I'd fly QA?

No.