No, not metric but certainly not SAE either. The threading on US military guns was identical to the French threading system and remained the same through the production of the Trapdoor Springfield. Many screws used 22 TPI.
Yes, that is essentially correct. The threading used by the National Armories is sometimes called the Springfield Armory thread system but it was copied from the French standard adopted by the French Committee of Public Safety, St. Denis Armory, in 1791-92. It had been in use for many years before that.