The International Criminal Court is seeking the arrest warrants on charges of war crimes and crimes against humanity over the October 7 attacks on Israel and the subsequent war in Gaza.
Yes, Putin has avoided those destinations so far. He even got warned by South Africa that they’d have to arrest him if he were to travel to a meeting there.
And if Netenyahu even lets Israel have elections. Before 10/7 he was already in the process of getting kicked out of office, the only reason he's still in power is 10/7.
Technically any member state, but they wouldn't refuse him if a non member state arrested him too. And I say technically because there's a few member states that support him and would likely not arrest him.