I think you'll find that the Leonardo Express, which is the train from Fiumicino to Termini takes a little over 30 mins and it's 14€ each way. But very efficient!
Trastevere is a good 4 km from Termini, so a bit of a walk, but definitely do-able, but I wouldn't say it's close, and would not recommend it at night time.
RE: Ladies! Which one of these man ,u would never date.