No, under your hypothetical it's still a crime, but it's not admitting to a crime. You haven't pled guilty, you are still asserting a defence to the accusation (that you own Moscow).

For governments, yes. Having that sweet legislative power is pretty nice.

(Yes, there's an international court. It's not exactly having a lot of teeth)

If you had a sufficiently powerful military to back up your opinion on the ownership of Moscow, then that would indeed be how it works. International law does not have courts with the same amount of power as "normal" law. If countries are at odds the options are basically a sternly worded letter, economic sanctions or military action. And, of course, the target of such action can strike back in much the same ways.

Understandably, not many countries are willing to enter hostilities with Russia.