Do all four pieces need to be painted separately, or can I paint them together?

Both approaches work. You can hang and spray them individually for easier masking and finish control, or clamp them together and paint as one batch if your spray booth allows. Separate painting gives you better access to seams and edges.

Will gap filler or seam tape be needed between the bumper and side skirt sections?

FRP panels rely on proper alignment and factory mounting points for tight fitment. After installation, inspect each seam under good light—most gaps close when panels are fastened correctly. If minor gaps remain, flexible trim tape rated for automotive paint works well; sand and prep the surface before applying your chosen finish.

Can I install this myself with basic hand tools, or do I need a shop?

DIY installation is absolutely doable if you're comfortable removing and refitting bumpers and securing side panels. You'll need basic fasteners appropriate for your mounting points—refer to your vehicle's service manual for specifications. Take your time with alignment before final fastening, and test-fit each piece before painting to avoid rework.