I've gotta agree, that does look awful. Is this the only area in the shower where the grout is cracking, or just the worst area? It looks tight at the bottom, then gets worse as you get further away from the floor, then seems to tighten up (narrower crack) as you get close to the ceiling/top of wall. Is that correct, or just camera angle? The tile just below the glass blocks seems to be misaligned with the one below it. correct, or again, camera angle?
That much separation in grout lines should not happen. Something may be going on that is causing movement of the tile backing. Could be any number of causes. Bowing of the stud supporting the wall, insufficient fastening to handle the weight of the tile walls, or use of improper backing on the tiles (ordinary drywall instead of "greenboard" or concrete board tile backer are some of the most likely issues. You need to be sure that the underlying structure is sound, otherwise you will put in work redoing the grout and it will be back like this in some months.
I would make sure the stub wall is straight and flat on both sides. Put a long (4-6 foot long) level on both sides and see what you get.
Bleach is your friend in killing mold. there is really no cleaning of caulking, just removal, cleaning the underlying surfaces and then reapplying good quality caulk.
There are hand operated grout rakes. There are rotary tool (Dremel etc.) grout removal tools. You will need both. Power tool for most of the work (unless you are a real glutton for punishment and want to do it all by hand). Hand grout rake for the tight corners etc.
By the way, the split tile on the top of the sill is not the best way to do that. The joint in the middle is an invitation for water to sit and then eventually work its way through. The sill ideally is one solid piece.
