The UK Hyundai Coupe Club

Haven't done it on my car but would have thought to put back on just push the prongs back into the holes, I would use fresh adhesive.

I have used Granville Black Silicone sealant to fix clear side repeaters in place, withstands extreme temps and permanently flexible, it takes a few mins to go off, easy to wipe off any excess off the paint- can get it from halfords

What colour are soraying the badges?

I sprayed mine, normal debadge process.

If you've got fine wet/dry, sand them down a little, just to remove the Chrome so the paint'll stick better.
Prime, Spray and Laquer.

I stuck mine back on using a bit of clear all purpose adhesive.
Not come off yet, survied jet wash, snow, frost, I even had a small go at removing them so I could sell them on.

Just be careful not to drop them once painted, even though I sanded/primed/laquered mine, the paint chipped when I dropped it. lol.

I would probably go for matt.