If I understand correctly (and that’s a big if given I’m not any kind of lawyer, never mind an international treaty specialist) the country which allowed the launch is responsible for the damages in situations like that. So no, it’s still their problem.

Only if the country has agreed to join that international treaty.

That's a great way to get your satellites "accidentally" hit in retaliation

China is the source of largest amount of space debris (as a result of testing their anti-satellite weapon). How will the US (or any other country ) know the country of origin of the space debris ?

The US (and presumably other countries like Russia and China) has a pretty robust tracking network that keeps track of pretty much everything in orbit above a certain size. With that info and when the strike actually happened it's pretty easy to backtrack to determine the possible culprits.

http://www.stratcom.mil/Media/Factsheets/Factsheet-View/Arti...

... in which case India or Taiwan would on the hook for it, if found out.