I'm a Canadian car seat tech who has flown with car seats many times.
1. Car seats must be approved for use on aircraft. The poster who said she travels with her seat and manual is absolutely right, just highlight the bit about airline approval before you go so it's easy to find when needed
I have only been asked on West Jet to show my certification sticker (the Canadian 213.X sticker) but never to prove the seat was approved for airline use. However, Britax seats are commonly used on airlines, so that may have been why.
2. Britax seats are a bit of a pain on aircraft because they have a solid plastic belt path. Other seats, like the Diono/Radian don't, so the aircraft buckle can be released easily. The trick to Britax seats is to ask for a belt extender and keep one of the release buckles outside the belt path. I taught this trick to a few flight attendants who thanked me profusely
However, I would never give up travelling with my Britax for the sole fact it has built in lock offs, and when I'm in Mexico installing my seats, I don't have to worry about how long it will take me
We used our Marathon onboard aircraft until DS2 was 4 years old. He's a little guy, so we kept him in the restraint and we were still within the airline's regulations.
3. The CARES restraint is loved by some, hated by others. There are many reports of kids "submarining" or slouching in the restraint and being choked by the chest clip. Definitely a situation where you want to consider all options before you go.
4. About rearfacing infants...the child restraint has to be installed as if it was being installed in a car using a lapbelt, so infants need to be rearfacing. There are some extended rf folks who cannot rf their children on an aircraft without obstructing the seat in front, so they ff for airline use only. This is mainly an issue with rf Diono/Radians because they are so tall and tend to install at a very reclined angle on aircraft unless you use the angle adjuster or brace against a bulkhead. On an aircraft, you are less concerned about head excursions and more concerned about keeping the child from being thrown around the aircraft...thus why there are no top tethers for ff installations.
I have found very supportive airline staff and people who thought I was a royal PITA
I found having my documentation ready, including my manual stating the seat was airline approved, as well as paper or digital copy of the airline's own policy on child restraint use on board very helpful. I'm also very clear on what I'm asking to do and how I propose to do it, staying within the regulations of the airline I'm using. Again, my experiences have been on West Jet, Air Canada and US Air, but from what I've read on car-seat.org and discussions with other car seat techs in my area, they are pretty common.