Can they stop me and check documents with no grounds at all?

Legally — no. Art. 19 of the Law "On Police" contains a closed list of grounds (resemblance to a wanted person, reasonable suspicion of an offence, territory under a special regime, scene of a crime, appearance or behaviour indicating possible involvement in an offence). A simple "I felt like checking" is not a ground.

In practice — yes, they stop people. Patrols operate in "routine check" mode and default to citing "general safety". Formally this can be stretched under Art. 19 (c) (special-regime territory) or (e) (external signs suggesting possible involvement). Arguing this on the street is pointless: courts rarely find a stop unlawful on the single ground that "the officer did not name a basis".

What actually works: if nothing follows the stop — no detention, no protocol, no seizure — the lawfulness of the stop itself is practically never challenged (there is nothing to overturn). If something bigger did happen (a search without a warrant, detention, seizure), then on appeal the absence of a clearly stated basis in the protocol becomes one of the arguments — and often a successful one.