I've had backwards facing seats on numerous flights - us domestic and trans-atlantic. FA's will check to see if the seats are "FAA approvced" in the US. It should say on the seat itself - if not, check the manufacturer's web site.

I always recommend ticketing a child for safety reasons, although the 10-50% fares seem to be a think of the past. I have always booked a seat for me two, starting at 12 and 16 weeks, respectively, and it's always been the same (cheap, advance, restricted) fare as adults. Perhaps full Y is different. If you choose not to get a ticket, show up with the seat at the gate. If there are empty seats, FA/pax are usually willing to shuffle to get you together. If it is sold out, you will just have to gate-check the seat.