"As I understand it there is also no proof that a child is safer in a car seat on an airplane than in just the seat alone, which is why there is on requirement for usage."
Incorrect, I'm afraid. There is plenty of proof that carseats are safer for turbulence and hard landings. The reason there is no requirement for usage is truly bizarre, and is based on the statistical probability of injury in commercial aircraft vs. private automobiles. The FAA does not require carseats because people who would otherwise get a free seat for a lap baby might choose to drive if they had to use a carseat. Since driving is statistically more dangerous than flying, they feel that making it easier to choose to fly best serves the interest of public safety. I've read transcripts of the hearing testimony; the logic just boggles the mind.
As to the rules, from the horse's mouth, go to the US code of Federal Regulations. The rules for carseats on US commercial airliners are in 14CFR121.311:
http://a257.g.akamaitech.net/7/257/....gpo.gov/cfr_2004/janqtr/pdf/14cfr121.311.pdf
In addition, if you are using a convertible-type seat, check for the FAA definition of "booster seat" at 49CFR571.213:
http://a257.g.akamaitech.net/7/257/....gpo.gov/cfr_2003/octqtr/pdf/49cfr571.213.pdf
(It is possible that a seat that the mfr. labeled as a "booster" is not the sort of "booster" forbidden by 14 CFR121.311; if it has an upper-body harness it probably *is* certified for aircraft use.) It's not a bad idea to carry copies of both of these sections of the law with you when travelling with a carseat.
Carseats must be positioned in a window seat or in the center seat of a center section row on a widebody. (This is so no one has to crawl over it in the event of an emergency evacuation.) Carseats may not be placed in exit rows (of course), or in the rows immediately in front of or behind the exit rows, either. Most carseats will be very difficult to install in a bulkhead seat, because the armrests do not lift.
BTW: if a child wants to kick seats, take his shoes off, and also get a pillow from the FA and put it in the seat back pocket.