Will this work if my truck originally had fog lamps?

No. This cover is molded without fog lamp openings. If your Ram came with fog lamps, you'll need the version with cutouts or you'll be covering the lamp housings.

Do I need to remove my grille to install this?

Depends on your approach. Most installs work with the grille in place, but removing it gives you better access to the upper fasteners and alignment points.

Can I paint this right away?

Yes. The primed finish is ready for color coat. Light scuff with 400-grit before primer or paint application is standard practice, but no heavy surface prep is required.