The whole edges are probably solid.

Hollow-core doors have solid edges that are about the same size.

Latex paint stays soft and will stick to objects on the shelf. This is why things like lightswitch plates and door knobs are generally kinda stuck to your walls and doors.

Chalk paint is trendy shit. It's soft and needs to be coated with something to not constantly rub off. The paint itself is extremely matte.

I'd use urethane or oil based enamel paint. It cures much harder and is generally what's used for furniture and cabinets. Clean up is harder, but doing it right the first time will save you time overall.

For a glossier finish you might need to sand between coats. I'd check with the paint itself once you've decided on it.

Once you've got your paint on you don't need to clear coat it. It'll just mess up the paint's curing.

Just take the door apart and put it back together the other way.

If the current paint is solid and not peeling or bubbling a standard thorough clean, maybe a light sand if really glossy and primer should be fine.

Fast, sturdy solution: Bolt some plywood over the outside. Caulk the edges. Couple coats of exterior paint. Stuff insulation into the wall gap space. Drywall the inside surface.

Temporary fix: Sturdy sheet plastic on the outside, stapled down. Insulation in the gap. Plastic sheet on the inside.