No. It is part of the space treaty that most nations have signed up to, that any part of a space craft remains the property of whoever launched it, and clean-up of it is the responsibility of the country from which it is launched.

Once burnt, yes, safe greenhouse gas. At least, no worse than any other combustion products. I mean, it would be nice if hydrogen wasn't such a pain, but we have to work with the universe we are given.

Methane leaks need to be contained to the amount practical, but they are doing that.

SpaceX has completed their mishap report, which states what they believe are the required corrective actions, actions which, it can likely be assumed, they have already completed. So all that is needed, from their standpoint, is for the FAA to accept their report, accept their corrective actions, accept the actions as done, and issue the launch license.

FAA could, however, decide against any of those things - that the report hasn't covered something, that other actions are required, that the actions haven't been properly done.

This is entirely in line with everything that both FAA and SpaceX have said.