Considering the rest of the barrel has steam or smoke (artistic representation thereof at least) she likely burned herself on it. She probably touched the silencer on the end after tearing through several mags at the range, the silencer and the barrel would be very hot after half a dozen mag dumps, especially with the silencer trapping so much heat by its very nature.
Judging by post #6722451, the girl on the left is Haruka and Sora's daughter. Not sure if that's enough to justify the mother_and_daughter tag though.
Yes, it is enough. Though it might be a good idea to make a tag specifically for non-canon children. We do have if they mated, but I don't think it would apply here since we can't tell from the image who the father is.
Regarding the weapon request, it looks like it's the Colt 1877 from the first two images with angry red lines drawn on it, and some extra gubbins under the barrel. All the lines of the 1877 are still there, though, so I'd feel comfortable tagging it as the 1877 still.
According to the commentary, these are the fast cruisers under the command of Tsuboi Kouzou during the 1894 Battle of the Yalu River. The front ship is the Yoshino but beyond that it's tricky, given a front-on view. The Akitsushima is probably the third based on the bow. Naniwa and Takachiho are nearly identical so I can't really differentiate between them.
