"Can transfer UR points to AA if you need it for flights. ​"

No, you can't -- at least not directly. But you can transfer UR points to BA, and then redeem for AA MileSAAver award seats, at BA's redemption rates.

If you also get the Citi/AA card and add your AAdvantage number to a BA redemption on AA, you'll still get your free checked bag and priority boarding.

Absolutely no reason not to get both the CSR and the Citi/AA card. But definitely get the CSR card first, and before the sign-up bonus is reduced.