Is the EASA RT License valid internationally?
The answer saying that &quot;Each country has their own governing rules regarding qualification for Private Pilot Licenses&quot; is of course wrong. The OP has specifically asked about EASA. The privileges of an EASA licence may be exercised by the holder in any EASA member country by virtue of § 11.1 of the Basic Regulation – Regulation (EU) 2018/1139.

if I want to rent an Airplane in another country in Europe (like Hungary), should I get Hungarian RT license? or my Czech RT license is valid for all EASA countries?

The latter.

is the PPL EASA license (with valid RT license) sufficient to rent aircraft in Europe? Or do I have to pass some test for each country?

The former (don't forget about the medical!). Of course, nobody in their right mind are going to let you fly their aircraft without having you checked out first, but that's a club / school / owner policy not something State-mandated.
In any event, ask your flying school in the first instance and the CAA in the second. Only a complete fool would rely on random stuff seen on the internet!