There are a few tiles that are loose, or have loose/lifted edges, and some tiles have chips/parts broken out. We still have a few boxes of the (original installation) tiles, so we can more easily patch these broken/missing areas, before laying the moisture barrier, rather than removing all the tiles, in order to make the floor even, with no dips or voids. Or is this patching not such a good idea? I'm thinking, this patching is a reasonable solution for eliminating the broken/missing tile voids, that would, otherwise, be under the wood flooring.

1. Yes, totally reasonable to just lay over the existing tiles.
2. Yes, lay down a vapor barrier. They sell thick mill plastic for this purpose at the borg. It has peel and stick along one edge and you tape it off wherever else you need to so you get a good seal.
3. Patch the voids in whatever way is easiest or don't depending on how deep the voids are. If it is just 1/8" tile thickness and you are laying in 3/8" or thicker T&G I wouldn't even worry about it.
4. Shoot it down with staples in the groove using the proper floor nailer for the thickness. Small ones for 3/8 & 1/2" and the big daddy for 3/4".

I've done this and similar a few times in some of my rentals and haven't ever regretted it.