Is there any possibility of recording the online pilots' voices while we are flying? I'd like to include my Squadron mates' voices in a movie, but I don't know if it is possible or not.

Teamspeak has a "record" function.

Or you could use Free HiQ recorderto record all sound as mp3; though feedback may be an issue on some setups

Do you know if that "record" function affects the frames per second while flying online?

No... Using the supplied codecs in TS, 5Kbits per Sec produces no noticable drop in FPS.

I recorded 20 players on a Co-OP for 1 hour, resulting in a 150MB audio file.

Usually people like to be notified when you're recording as they might say something 'not for the record' . Also when recording TS places a marker next to your name, so everyone else can see.