What you're showing in the pictures are the nakago (tang) of Japanese (or Japanese style) swords, showing the mei (signature). Typically these show the smith attributed, or a date, or sometimes a particular achievement in testing (such as the number of bodies cut during tameshigiri/suemonogiri). Without seeing the way they're mounted, or even which side of the nakago the mei is on, it's not easy to say what the "type" of swords are... but most likely from looking at them, they're a katana variant. The amount of rust is typically an indication of age, so shouldn't be cleaned off... the last image is either a much newer blade, or it's been (foolishly) cleaned at some point recently.
For anything more than that, including their categorisation, we'd need a fair bit more information.