To glue to other Veranda pieces, you can use Clear PVC cement. To glue to other substrates, I.E> Wall, OSB, Brick, Construction adhesives work. Always test before use.
Yes, water proof and moisture resistant.
I would say no unless you use a paint type of stain
yes, paints made for plastic work best
Both sides are smooth, so you can use either side.
It can, but it will melt if the router generates much heat. I have not seen large air voids (not saying that there never are any), but the material is a bit porous, so the routed surface will not be the same hard smooth texture as the manufactured surface. That would probably not be a problem if you're going to paint it, but if you leave it exposed, it will look different and probably hold dirt more easily.