Do I need fasteners or hardware to install this?

The guard mounts at factory points, but hardware specifics aren't confirmed in the product data. You'll want to have stainless steel bolts and washers on hand, or verify what came with your original bumper guards before installation.

Can this guard be painted, or does it stay chrome?

It ships with a polished chrome finish. If you prefer to paint it to match your bumper color, light sanding and standard automotive primer and paint will work — test on a small area first to make sure adhesion is solid.

Will this guard add any noticeable width or stick out from the rear?

It's designed with an OEM profile to sit flush with the MDX's rear bumper. Exact protrusion isn't specified, so a test-fit or photo comparison with factory guards is your best bet before committing to permanent installation.