Re: Remington 51 .380
Jack First Inc (605-343-8481) sells modern reproductions of Remington 51 grip panels and backing plates. Not sure if rivets are available, but the parts section technicians who answer the phone can locate that information for you in a few seconds.
W.H.B Smith's Book of Pistols and Revolvers contains detailed and relatively foolproof instructions for disassembly. Instructions can also be found in the NRA Firearms Assembly books.
Firing is generally not recommended these days. The breechblock is a relatively light part and very slightly prone to fracture. This renders the arm unusable. Replacements are not available, and the youngest specimens are over 80 years old, with all the risks and uncertainties attendant to metallurgy and aging.