as the title reads the mirror/prism mirrors behind the lamp has some "fog" on it. It appears to be dirty build up with (smoke girlfriend not me) dirt and smoke. IS it POSSIBLE to clean this mirror? Any good tips?
yes, but than you'll probably need to align the entire light engine from bulb to screen.
I can't imagine wiping the mirror down with anything that won't scratch it.
Also? The REST of the optics are probably also coated with XXX.
I can't imagine this set still working correctly. It is a rear projection LCD type. SONY used plastic filters in the light engine which discolor and render the picture unwatchable. SONY lost several class action lawsuits over this tech. Sony is a multiple-patent holder in this space. They never learned since the SAME defect doomed the incredible SXRD models which were the follow-up to the projection LCD stuff.
Junk it out, buy an OLED and carry on. The 55" OLED sets are getting affordable and have a better picture. And no internal optics for your GF to mess up with her 'habit'.