1) You can, but it's not likely to stick...or match the color...or remain uncracked for very long.
2) You can, but because it's full of grout, the silicone will be very thin once it's tooled and it'll be likely to crack. A very thin bead of silicone puts all the stress onto a very small part of the grout body. You really want to remove the grout so that it can be filled with silicone. A full bead of silicone can deform much more than a thin film can before cracking or pulling loose from the corners.
3) Yes, remove the grout.
3a) The individual walls move independently due to normal expansion and contraction. Grout has very poor elastic qualities; slightly better with the admix, but no where near where what 100% silicone has. Even with the admix. I would recommend against grout, but you're free to do what you like.
3b) Yes, my recommendation.
4) Recommendation is to remove grout and replace with 100% silicone that can remain intact as it deforms with individual wall movement.
5) You don't need to wash with vinegar. You brought it up. If you've got a little grout film, this is one method of cleaning it off. If all the grout you need to remove can be done with a grout removal tool, then just use the tool.
6) You're substrate is likely to be cracked in the corner as well.
7) I like using an oscillation tool like a Fein MultiMaster with a grout removal blade (actually, I don't like removing grout at all, but when I'm forced to, this is the tool of choice). But I've used every tool at one time or another for various reasons.