Tile – Spacing when transitioning tile size

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.

Pry that tile up, it sounds loose on that corner - i.e. not only unsupported, but some of the thinset in contact with the tile did not adhere.

That looks like unglazed clay tile (aka mexican clay tile), which you must moisten on the bottom to get it to adhere well. If you don't, the tile sucks the water out of the thinset before the thinset can bond, and you get what you have with that "klonking" tile.

If it was just voids at the corners, you could just "pipe" some more thinset under the tile with a pastry bag, but after watching that video, I would pry up that tile. Hopefully you have some spares.