Good questions, but I have not been able to find the answers. Looking through the records of events and CMSRs of the regimental quartermaster, I haven't been able to find out. The Crescent was a popular militia unit and its drills were publicized in the newspapers as an event to see. Maybe they had their arms very early on. The newspapers made much over the wealth of the members... maybe the arms were raised by wealthy benefactors rather than government? My only lead on the "when" are newpaper accounts of the departure from N.O. in March stating that the regiment was "well armed." I know that I have read accounts that some regiments left for war with whole companies unarmed.