"how do you make a black background - can i just do it in fcp with a solid and make it like 2mins long or whatever i need? How best to apply it in Resolve 9 - in the time line or specialty node type operation?"
If you have read the said manual already, you would know how to apply that in Resolve. As I mentioned before, however, there's a quick and dirty method where you would just qualify the BG, and HILITE on to see your BG in black. You just need to change the setting in the CONFIG window so that Resolve shows the key as black instead of gray.
If you'd like to follow what Resolve manual says, then yes, you could make the solid black clip to whatever length you want to composite in Resolve. Better make it longer than you need since you can trim it in Resolve.
"Also, when you said "the graded shots for the vfx people to use", exactly what format/way do you render that out?"
That depends on what your vfx guys want per project. Ask them what they want..
Nook Kim
http://www.nookkim.com