Regarding chain skipping, the only time I've had that problem was with a new 7-speed KMC chain on a hybrid with one of those dreadful Shimano MegaRange freewheels -- one of those things with a massive jump from the 24T sixth cog to a 32 or 34 bailout granny gear. It's almost impossible to shift and maintain a smooth cadence between those sixth and seventh cogs.

My mid-2000s era Globe Carmel comfort hybrid/errand bike has an unusually long wheelbase, like it was intended to be a cargo bike but Globe (Specialized) decided to make it a comfort hybrid instead. No prepackaged chain is long enough so when I installed a new chain I had to splice two new KMC chains of the same type together.

The new chain began skipping in the three smallest cogs, worse with each smaller cog. The freewheel was far from worn out, so that didn't explain the skipping. I put the old chain back on -- no more skipping, although it was sloppy from wear.

Even though the freewheel didn't look worn I decided to replace it. But a user review on Amazon suggested the problem was with the Shimano MegaRange design -- the spacers between the cogs are too large in diameter. No problem with the larger cogs, but as you reach the middle and smaller cogs the wider parts of the links at the roller hinges (assuming typical Figure-8 shaped chain) would contact the spacers and push the chain upward, causing skipping. So it was essential to use a narrow chain (labeled as such by Shimano and KMC).

I happened to have a couple of worn "narrow" chains from another bike and decided it was worth a try. Sure 'nuff, even the badly worn narrow chains, spliced together, solved the skipping problem on the MegaRange freewheel.

But I hated that MegaRange freewheel anyway. So I replaced it with a SunRace 14-28 freewheel, which worked fine with the new non-narrow KMC chains I'd spliced together. That setup is still on the bike two years later, no problems.

I've hesitated to discard even noticeably worn "stretched" chains because they still worked fine. I just replace them every year or so depending on how much the bike was ridden... mostly because we're supposed to? I dunno. I finally got over my thrifty hoarding and threw away some old worn chains. If I had an ultrasonic cleaner I'd clean 'em up and convert the old chains into jewelry or sculpture and something to smack the hoods of cars that pass too closely.