Lexan can be cut with anything you want to cut it with. handsaw, circular saw, dental floss. doesn't matter. it isn't a hard substance that needs a special blade.
we screwed it into the wood. and like we recessed the holes...i think that's the term. so like the top of the screw heads sit below the surface you know?
if your sheet is to thin to countersink, like less than half inch, than you can use liquid nails, or some other adhesive, or carriage bolts if you dont mind a few bumps
score it with a razorblade and snap it off. then drill holes in it to fix it to your box frame. but don't press too hard with the drill, or you'll crack it to the edges, slow and steady.