Welcome to FT. The other post was good advice, I'll just add a little to your specific questions.

1. Yes, you can hold as many as you want. But it is not always wise to credit miles to the airline you are flying. Lots of people sign up for many programs, but do some research before you fly about which program to credit your miles to. It's better to have a few programs, like one in each alliance as the previous post said.

2. You don't move the points. The alliance lets you earn on partners in the alliance (if the fare is right as discussed above) and use the points to fly on other partners in the Alliance. So you like Japan Airlines - if you fly them again you can credit those miles not only to JAL, but to other partners in One World, like AA or British Airways or Cathay, as long as the fare allows it. Similarly, if you have a bunch of AA miles, you can use them to fly not only AA, but also Cathay, Finnair, LAN Chile etc. Also, each airline usually has a couple non-alliance partners. Like with AA you can use your miles to fly Hawaiian Airlines.

3. AA, UA, DL charge 25k miles roundtrip for almost all economy flights in the lower 48. One difference is British Airways, which has a distance based program and as part of Oneworld you can use their miles on AA flights. Also Southwest, which has a cost based program. Look through the link above and you'll get an idea of one that might fit for you. For Int'l, AA has some great off-peak redemptions. UA is popular cuz it allows a stopover and open-jaws. Again as mentioned, AA and UA are two of the more popular ones to use, especially if you're in Chicago.

4. Earn and burn.