Yes, you can make FRP (Fiber Reinforced Plastics) with chopped fibers. It's very common in things like boats, fiberglass car bodies, etc. You can even get some anisotropic properties depending on your processing (think of OSB (Oriented Strand Board) sheetgoods you see @ Home Depot).
You generally won't get nearly the same kind of performance as a tow or pre-preg assembly though. You can't get your fiber fraction as high, and because you can't control the fiber orientation as well, so you can't take full advantage of the fiber stiffness & strength. But the processing can be much easier, and the fracture toughness can be much better IIRC.
Joining to composite material is typically a combination of adhesive & mechanical fastening ... ie. glue & screw. Actually, ussually bolts or rivets rather then screws. Of course, care must be taken to account for the load concentrations.