For the skipping freewheel sprockets, this picture shows one tooth having been given "the treatment", a very small bevel that is preferably at about 30 degrees to the driven side or "edge" of the tooth rather than at purely a 45 degree angle. The angle is not really that critical, only that the bevel can be very small and yet still effective at preventing the chain's rollers from hitting the sharp corner and "failing to engage" between the teeth (what actually causes the skipping under load).

---------------The "driven side" or edge of the tooth is the side/edge that the chain roller pushes against-------------

Notice in the photo the beveled top-most tooth stamped "ba". This sprocket is not very worn at all btw, but is a sample showing a generous bevel.

BTW, this IS a cassette sprocket, and yes, these too can be saved. I often find mtb's that are ridden mostly in the top gears on the local river bike trail, with tell-tale severe "pocket" wear near the base of the driven side of the smaller sprocket's teeth.
Only when the chain is allowed to stretch severely does this wear extend toward the top of the teeth (which at that point is usually not repairable).

The OP's Sante 7sp freewheel looks very typical and very fixable in my estimation.

I could almost agree with CroMo Mike's "Life's too short to figure out why cogs skip", but finding good freewheels with desirable ratios is becoming less easy as one might conclude from the prices that some of them now fetch (and I am now only rarely finding good road bikes at thrift stores these days). The grinding fix is a quick 5 minutes and they then usually work like new.
The Suntour freewheels I agree are excellent, and I prefer to use 9sp HG or C9 chain with all types of Suntour freewheels for the easiest, most-forgiving shift quality.

Using new chain does not prevent the pocket wear, but if one rotates between 2 or 3 chains every thousand miles or so, then the chains/sprockets stretch/wear together and thus can remain in service together for a very long time, perhaps well upward of 10k smooth miles of riding in average road conditions (around here, it can be longer because of mostly good weather).

These days, I usually don't even remove the freewheel from the complete bike when doing the grinding, as the sprocket fix is most often part of a quick "get 'er on the road" tune-up for evaluation of the bike's riding characteristics or to be flipped to students who leave their bike outside, treat the bike as a disposable entity and have only $150 to spend. I hold the dremel tool parallel to the axle and use a ~3/8" diameter stone wheel, rotating the freewheel backwards to access each tooth of the affected sprocket.
The Dremel grinding dust doesn't seem to have any effect on the drivetrain that I could notice or would worry about myself. Of course one can also take a sprocket off of the freewheel and use a bench grinder, that's what I used to do before I wised up.

As far as the 980 derailer is concerned, I found it to shift very well with standard road gearing. Sure it's made for use with older, stiffer chains, but mine shifted quite good using HG chain.