Tile – Why nut with gasket on tile cutter wheel

All you need to do is leave the grout to dry before getting it wet. The instructions should tell you for how long. As you and others have pointed out drying and curing are separate things.

While you can use the shower after the grout is dried you may need to leave it for a day or two after it's cured before sealing. You don't want to seal any moisture in.

It sounds like your goal is to avoid cutting any tiles in the dimension from the 48.5" + Entry (from your pictures). 12X12 tiles won't necessarily be 12". I grabbed an extra that I had in the garage and it is actually 11.75" but is sold as a 12" tile.

As mentioned in the comments, I'd buy the tiles that you like first. You could actually buy all the tiles you are going to need and lay them out in that area with the grout spacers (little plastic spacers that keep all the tiles evenly spaced). Then you could pencil in your wall at exactly the location you'd need to keep from cutting tiles (in that dimension at least... you can't do much about the space between your front door and closet door).

Note that the tile shouldn't butt right against the wall. Your floor/molding trim will cover the small gap between the tiles and the wall.

Hope that helps. Good luck! Tiling is actually not that bad and can be fun.