first question I belive, I would trowel compound over any knicked areas that are concave enough to accept some filler to smooth it out. Use spackle if you want as it will not shrink.
Second, I would re tape those areas and get out that contaminated old compound and add new and do it the proper way. I would and always use fiberglass tape on walls and seams and paper in corners. I find fiber does well and will move without breaking, but it will not work well, at least for me in corners.
After all patched and dried, then prime the entire surface in prep for your new texturing.