Wanted: Repair of Granite Crack & Molding Gap

There are elastic gap fillers that work nicely for crown molding that expand and contract with the temperature, which is what you need. I wouldn't try tape. This happened in my house too.

If you're not good with caulk you can either practice, practice, practice, or hire someone who is good.

Regarding the hairline crack in slab granite: This is a risk inherent in slab granite counter tops. The veins the run through granite are relatively weak compared to other parts of the rock. (Assuming damage is not from deliberate vandalism) If this is a high-end property the slab will need to be replaced eventually, there is no avoiding it in my opinion.

You can delay that expense, perhaps by a long time, by caulking with a paintable caulk, if you can't find a commercially available product in the right color. Allow surface to dry for a day or two before patching, and then keep off of it for another day or two after. Paint it with acrylic paint, I would use artist's colors in tubes and mix to match (but then, I'm a fine arts painter). Be sure to let the paint dry to evaluate color match.

If patching the crown molding was too tedious for you, then both jobs really should just go to someone who will do it right.