Does the US government have any authority on this? I thought there were a dozen countries launching satellites now.
It's establishing (assuming it gets passed and signed) the work for a demonstration program on active debris removal from orbit. It's not imposing the US government's will on anyone else.
Say China decides to flood a particular orbit path that a US company was planning on using and went through all the approvals for.
Is the China stuff now "dangerous debris"?
It depends on who you are, who you're messing with, who your friends and their friends are, whether they stand to lose face or can pretend they didn't notice it, etc. The US once tried to steal the wreck of an entire Soviet nuclear-armed submarine off the bottom of the ocean (and mostly failed.) The Soviet response was a request to stop talking about it, because it wasn't worth a war and Soviet leadership didn't want to explain the incident to their own public.
Anyway, China is already toying around with the first sort, and they didn't ask anybody for permission. Their 'authority' to do it is being a sovereign nation.