From what I've read, turns only seem to use the notes in the key, so if I'm in C Major, what would be the notation for a turn with G-A-G-F#-G ?
It would probably be better to just write out exactly what you want instead of using a turn. The purpose of ornaments is to quickly notate common patterns to "ornament" the melody. Deviating from the standard can lead to confusion especially if the alteration isn't very well known. This shows how a turn would be notated without actually using the turn notation.