I'm also new here but not new to the collecting world, however I will defer to those on here with vastly more experience then me. These are my opinions-
Should you clean it up- by that do you mean wipe off the dust or do you mean sand down the mold lines, repaint it, etc? A simple cleaning cant hurt it but doing a major refinish could hurt any value (even minimal) that this item has- I would assume even if its not screen used that an ILM proven prop must have some intrinsic value. So my opinion is dont do anything that would modify its current finish.
I also base this off years of real world experience involving guns. I cannot tell you how many Colt single actions, Lugers, WWI/II 1911s, etc that used to come into my fathers store that would have been worth thousands only to be worth hundreds because the owner decided the weapon looked "too beat" and had it refinished (or in the case of a cavalary Colt SA they actually took a wire brush to it in order to make it bright and shiny- destroying the natural patina and turning an easy $8-10k pistol into <$1500). If I have learned anything from places like RPF is that condition is everything and collectors want the props to reflect the beating they took (after all if you want pristine "factory fresh" props then you are talking almost exclusively about hero's or prop reps- and even hero's will show dings and dents from use)
As for screen time I will defer to better experts then me on that matter. I would assume it would be very hard to know for sure unless you found a prop list from when ROTJ, etc was filmed that states blaster TS 95 was used in X scene. But again I am just learning the ins and outs of this whole prop thing (and Star Wars is not really a specialty of mine)