Not sure about M-1 part but generally, I-693 can be submitted later in the process. Many get request for evidence (RFE) if not submitted initially. Ideally, you want to submit it initially becausd RFEs delay case processing. Sometimes, USCIS issues NOID (notice of intent to deny) or outright denial instead of RFE. Medical typically takes a few hours to arrange and do, at least in big cities.
Good luck!