Look up “star grounding” for a general idea of what to ground to which and how. Basically, everything should be grounded back to a single point at your wall (or in the case of two circuits, at your electrical panel), and you should avoid creating any loops in your ground path. A loop acts as a big inductor, introducing electromagnetic interference into your less-than-ideal ground.
To answer your questions specifically,
(1) Your spindle should be grounded to both. I’d probably ground the spindle to the VFD, then the VFD [is already grounded] to the wall. The machine will be grounded to the wall on a separate branch of the star ground.
(2) If the sheathing is carrying ground to the spindle, it needs to be connected at both ends. If the spindle is grounded elsewhere, then only connect one end of the sheathing (the end closer to the wall).
Avoiding ground loops can be tricky while you’re getting your head wrapped around the idea, but it’s straightforward once it clicks. The important thing is that each component has one and only one path to ground.
In general, (a) ground as many things to the wall as possible, through a ground prong in their power cable, (b) don’t connect anything that’s already grounded to anything else that’s already grounded, and (c) ground anything that you can ground.