No, you always book award flights with the airline that you draw mileage from, either by using their website and/or you may need call them up. Each airline operates their own frequent flyer program and you can not interchange or combine miles from one program to another. In your case, you can redeem US miles for flights operated by UA if and only if you have sufficient miles in your US account to make such redemption. Please invest sometime to read and study the basics about airline mileage programs and airline alliances.

In terms of which credit cards to apply, I'd suggest you first come up with a goal then try to see how many airline miles or hotel points you'll need to support such a goal, either as an learning example (for case study) or real life goal (so that you'd enjoy the travel experience in addition to the learning).

You need do some home work in order to achieve some meaningful goals that are best for you - b/c you know yourself best.