I need a camera that runs at 24P and can shoot with a shutter speed of 1/72 second. Why? I'll be shooting 16mm film being projected with a 3 bladed shutter. Can the FS100 do this?
No - one of the things that separates the NEX-FSx00 series from the 'professional' cameras are things like ECS - Electronic Shutter Control. This gives you fractional shutter speeds to two decimal places (tautology I know, but you get the gist).
I've checked with my EX1-R and I can dial in (for example) 72.01th of a second, so you'd be able to tune it slightly.
If the background is projected, you don't need DoF and in fact that could be a disadvantage, so I'd look into hiring an EX1 or EX3 or something of that ilk. But wouldn't let that put you off getting an FS700 unless it was a regular thing.
No, it can't. The FS700 jumps from 60 t0 100 just like the FS100, based on my experience with a late prototype. I used 'FSx00' to mean both 100 and 700.
Ralph two cameras Im familiar with that do have the ability to do this are the Panasonic AF100 and the Canon EOS C300 - I only add them here because as its been stated the two you enquired about cannot and thought you might like an alternative.