Hi guys I had problem with skipping chain, I changed the cassette and chain but the problem didn't solved. I assume that problem is in the chainring. Can you tell me is this chainring worn?

Your chain rings look fine . Maybe what you need to do is to adjust your rear derailleur ?

Myb that is the problem, because this happens on 2 heighest speed which I use the most. Also last time when I was at local bike service the repairman took out 3 links from chain for " better chain tense" could this be problem too?

That middle ring is definitely worn -- it's got the shark fin look. I assume that's the one you use a lot and skips? I'd replace it and keep a closer eye on your chain wear.

No, mostly, I use the big one,

The teeth don't lie If you mostly use the big one how did the middle teeth get so worn?

edit: In your OP you said you had a problem with skipping and then you changed your chain and cassette. Normally if a chain and cassette wear together they will not skip until you change the chain. Did you change the chain and cassette at the same time?

Because I am not the first owner of this bike
edit: Yes, I changed both at the same time.

i vote for a new small chainring. you never know how the previous owner really rode the bike, or how far, under what conditions, and the level of maintenance provided.

There still some life in the chain rings , I had see worst . If the OP want to change the rings he also have to replace the cranks for being a low level set . I would make the derailleur 's adjust first since the OP said it happen on two bikes .