the XIII is an assembly mark; most of the parts on and individual gun would carry that mark so that when assembled all would fit. Portions like the lock parts would be case hardened in batches and you could then sort out which piece went with which gun. HM or WH is probably the barrel maker. There is a Birmingham view and proof mark on the exposed part of the barrel. Can't tell you what the other marks are and can't read the word(s) stamped on the bottom of the barrel
cheers mooncoon