Do I need fasteners to install this, or does it come with hardware?

Hardware is not included with the bracket. You'll need to source the fasteners that match your vehicle's factory attachment points—check your service manual or have a dealer confirm the bolt size and type before ordering hardware separately.

Can I install this myself, or do I need to remove the whole bumper?

Depends on your access. Some installers can swap the bracket without full bumper removal if you have the bumper cover already off. Test-fit first—if you can't reach the mounting points with the cover in place, you'll need to unbolt the bumper assembly.

What does this bracket actually do?

It's the support structure that holds your bumper cover rigid and aligned to the frame. Without it or if it's damaged, your cover will sag, rattle, or sit uneven. This is a structural piece, not cosmetic.