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The drivetrain (chain? gears?) of my E-bike started to make loud clicking sounds, with the impression that the chain is skipping over teeth. The gear switching itself still works well.

I have tried to regulate the rear gear mechanism by adjusting the position screws but failed to make any improvement. The chain seems positioned properly.

I started to think, maybe some parts would require replacement. Could this possibly be for the bike that has been traveled only 400 km so far? It was rather cheap for E-bike from the other side, and on flat terrain it was mostly used on the same (fastest) gear.

Could some parts be already worn if low end? If so, which parts are likely to be?

Yes it can and I've seen it before, but the problems you describe sound like issues which could be fixed with a simple gear tune rather than being caused by worn-out components.

The only one that I've seen wearing out that quickly could largely be blamed on the riding style of its owner. He was a heavy rider and reasonably strong, so he was someone who would put more stress on any drivetrain. He also had a tendency to ride with the motor on full assist at all times to allow him to get over any hills without having to shift out of the 11 tooth cog at the rear. The load that he was putting through the drivetrain combined with the tiny cog taking all of the stress meant that components wore out very very quickly.

He came in for new chains and cassettes (couldn't just buy a new 11 tooth unfortunately) a few times before I found a cheaper, more permanent solution for him. We replaced the chainring with a much bigger one and put on a cassette with a 13 tooth as the smallest cog.

Even for a low end eBike using 400km will not wear out drivetrain parts.

If the chain was slipping over the sprockets, you would feel the cranks and pedals slipping forwards. This tends to be sporadic and makes a loud clang or crunch.

If you are hearing a periodic ticking, It's likely the rear derailleur indexing needs adjustment. From your post it sounds like you adjusted the limit screws rather then the indexing barrel adjuster.

Try following a derailleur adjustment procedure and see if that fixes the problem.

I have tried to regulate the rear gear mechanism by adjusting the position screws but failed to make any improvement.

That's almost never the adjustment that the rear derailleur needs. Those screws are called the limit screws, and they set how far in and out the derailleur can move. All they do is stop the derailleur from moving the chain all the way off the cassette on either side. There's basically nothing that causes those screws to move on their own so, assuming they were set correctly when the bike was built, they should almost never need to be touched. The symptoms that do mean they need adjustment is that either the chain is falling off the top or bottom of the cassette (derailleur able to move too far) or that gear changing is just fine, except that you can't change into the smallest or biggest cog (derailleur not able to move far enough).

The correct adjustment is to use the barrel adjuster to get the correct cable tension. That very often is needed on new bikes, because the cables tend to stretch a bit after they're installed. Argenti Apparatus has already posted a video so I'll not go into more detail than that.

Take the chain off and thread it through the rear derailleur properly.

It happened to me - there is a small guard near the top cog and the bottom of the rearderailleur, I threaded my chain on the outside of it (easilly done) chain slipped as described.