We are flying DFW/MAD on AA36 and then onward to Rome on AA5663 (IB codeshare). These are on separate (but linked) PNRs because the TATL is coach with SWUs, and MAD/FCO is award.

Which terminal (4 or 4S) will each of these flights use?
Which of the 3 lounges will be best for us?
Will I have to deal with customs and immigration, or will I be "in transit?"

Thanks for your help!