[I noticed a piece of metal that had broken loose that sets between the hammer and firing pins.]
[What is this piece called and can it be repaired or replaced.]
That is the transfer bar section of the selector, and Savage no longer will sell the replacement parts.
In lieu of the replacement parts, however, Savage will sell the upgraded selector - which is the later style hammer with the pivoting nose.
tblake - Your Model 22-410 has no serial number because it was made pre 1968 - actually pre-WWII (production started in 1939), like my Stevens Model 22-410 Tenite version, below.
My OTHER 22/420 is a later (1951) Savage Model 24-B .22/.410.