Can i pay with debit card in apple store in US? Even if i am from slovakia?

I can't tell you yes or no and I doubt anywhere in the documentation will say yes or no - Even for other services Apple isn't specific at the individual card level (e.g., Payment methods that you can use with your Apple ID - Apple Support ). I suspect they will as long as it is going through one of the major agencies. I have used our bank's Visa debit card in Europe, Japan and New Zealand with no problem anywhere.

If you want to see what Apple USA has to say about payment methods look here, but I suspect it isn't specific to the level that you desire --> https://www.apple.com/us/shop/help/payments

Do you mean a physical Apple Store? I don't see why it shouldn't except it probably has to be affiliated with one of the major financial institutions such as Mastercard or Visa. I know our debit card with a VISA label on it has worked in multiple countries around the world.

If your debit card has a VISA logo on it then it will probably work as well as ours does when traveling.