Both guns are/were U.S. muskets, made at Springfield Armory. The 1842 (dated 1850) appears to be in fair shape, though there is something wrong where the bolster meets the lockplate; there should be a perfect fit there.
The Model 1816 (made in 1823?) is a basket case and I doubt it can be even repaired, let alone restored. It began as a flintlock and at sometime, possibly in the 1840's, it was converted to the percussion system by the bolster method. Most of that type of conversion done for the government by private contractors and there is some variation in the actual work. It could also have been converted at some point by a gunsmith or by a company that bought the guns when they were sold as surplus. It appears to have been converted to a shotgun, a fate all too common for those old muskets.