- Maj7 - ionian or lydian would give it a "fusion" sound.
- Min7 - dorian or aeolian.
- 7th - mixolydian/blues/minor pent
- 9th - 9ths are usually transition chords, so you could play pretty much anything. It depends on the overall chord progression. Same thing for sus chords.
#2 Yes.
#3 You could, but it would sound like crap. C Ionian would work, but B and D Ionian have different key signatures.