Flooring Tile - removing grout, when to caulk vs grout

Hi, new to the forum and trying to fix a leaky shower stall. I've removed some of the grout...do I need to remove grout the thickness of the tile (e.g. all the way to the board underneath? (That's what I've been trying to do, but some of the tiles are spaced very close together so it's been tough with the grout saw.)

At corner joints and where the tub base meets the wall, I'm pretty sure that's where I use the caulk vs. grout. Have I got that right? (I had a professional re-do the grout to fix leaks a couple of years ago and they used grout at the bottom joint and corners -- of course it now leaks..I don't understand why they would have done it that way.)

Thanks. Good site.

If this wall tile has a thin grout line you want to get about 2/3 of the way in for grout removal, being that the new grout needs to get as deep as possible into the joint to gain a permanent foothold. A top coat will fall out in short time.
Caulk all the corners and along the bottom of the tile where it meets the shower base. No grout, with seasonal movement it will crack open again.

I have re-caulked the corners in my shower and it has re-cracked two weeks later. Any thoughts why this continues? It's happening in both back corners of the surround (the corners at the ends of the long wall) and seems to be connected to cracking on the walls above the tile surround. The cracks run verticle up the corners, stop about 3 inches above tile then make 90 degree turns to base of window trim. Looks like it may be a bad drywall seam.

I did try to remove debris and clean the area before caulking...twice now. I also repaired and painted over the possible drywall problem several months ago.