i watch6

You do need to own an iPhone.

The Cellular + GPS Apple Watch shares the iPhone's phone number, and the carriers that support the Apple Watch charge a monthly fee. In the U.S. the fee is $10 per month. Here is a list of carriers that support the Apple Watch:

https://www.apple.com/watch/cellular/

I do not see Slovakia as having a carrier in the above list.

See the link I provided above. If a Slovakia carrier is NOT listed, then you cannot use a Cellular Apple Watch in your country.

And as the carrier MUST support the iPhone & Apple Watch together, because the Apple Watch shares the iPhone's phone number, you CANNOT just use an independent carrier.

The GPS only Apple Watch can do Everything the Cellular model can do AS LONG AS your iPhone is nearby, where nearby is generally somewhere in the same moderately sized home. The Cellular model allows you to leave your iPhone at home while you go for a walk, run, bike ride.