How do we decide who gets to sit on the "reasonable" court? And how will its decisions be enforced against those who prefer not to recognise its authority?

What does it mean to be "somehow connected to" historical actions? (Is today's Spain responsible for the fate of the Incas? Is Italy "connected to" abuses committed by the Roman empire?)

I don't know where/how to draw a line. (Fortunately, I'm not in a position to be asked to do so.)

Sure, they are hard questions. My point is that confronting them is pretty clearly a better thing to do than dismissing them.

IANAL, but I think that the concept of 'successor state' is well established in international law.

As distinct from a "continuing state", yes.

https://en.wikipedia.org/wiki/Succession_of_states

Ah, but:

"There are several recent examples where a succession of states, as described above, has not been entirely adhered to. This is mostly a list of the exceptions that have occurred since the creation of the United Nations in 1945. In previous historical periods, the exceptions would be too many to list."

Seems like there's going to be scope for endless debate here... at least the lawyers should do well.

Right, and what do the ex-USSR states get from the USSR's successor state Russia as compensation?

I believe this swamp would be bottomless, and not every nation or victim who suffered from wrongdoings of others would get paid anyway.

Edit: victim

Actually there were reparations.