Yes
Caulking can be done either before or after painting depending on how steady a hand you have. Be sure to use a "Painter's" caulk, which is latex based. Silicone based chalks can NOT be painted over.
Polyseamseal silicone caulk would be the best caulking to use with bathroom tile, if you're not going to pain the caulk. If you desire to paint the caulk, MAPEI latex caulk would be best to use with the bathroom tile.
When it drys you should be able to rub it off with a rag or your finger.
you can paint over latex paint with latex enamel.
use your nails, scrape it off gently with a flat head screw driver...?
No. You should scape out the old stuff before putting in new. If the original stuff is failing, anything you put on top will be on a bad foundation. Nothing lasts with a bad foundation.
Put tape over open end. Keep caulk from freezing.
Yes you do, you wouldn't want to smear caulk all over the place.
It depends what kind of finish you will put on it, and whether it will be indoors our out: Indoors, latex paint: use latex wood primer Indoors, varnish: no primer required but can be stained, may need multiple coats Indoors, oil base: use an interior oil base primer Outdoors, latex paint: use an exterior latex wood primer Outdoors, varnish: no primer required but can be stained, use exterior varnish Outdoors, oil base: use an exterior oil base primer It depends what kind of finish you will put on it, and whether it will be indoors our out: Indoors, latex paint: use latex wood primer Indoors, varnish: no primer required but can be stained, may need multiple coats Indoors, oil base: use an interior oil base primer Outdoors, latex paint: use an exterior latex wood primer Outdoors, varnish: no primer required but can be stained, use exterior varnish Outdoors, oil base: use an exterior oil base primer
Usually caulk is not intended to be terribly strong, it's intended to fill holes, sometimes ahead of painting. A pure silicone will be pretty strong. A siliconized latex is also pretty strong, and can usually be painted over. If you want strength, look into construction adhesives. They're strong enough for things like bonding subfloors to joists.
Yes you can, but it is a cleaner job if you remove the old caulking (as much as you can) and reseal it with new caulk.