Thanks for the kind words Mike.
It takes a lot of guts to install 18" stone tile on a floor as your first installation, congrats for that.
Thin set and thin set mortar are the same thing. It comes in "dry-set" or unmodified, and modified. The modified version contains acrylic or polymer additives to enhance its performance and is required in certain instances. Both varieties come in white and gray color. White costs a little more and is desirable when installing light colored stone tiles. The color does not change the performance per se.
You will definitely want to install a crack iso on that crack, or a membrane on the entire floor. Although I use Ditra most of the time, this may be a job for NobleSeal CIS if you have expansion joints or control joints in the slab. CIS allows you to bridge the joints with the tiles so that it does not disturb the tile pattern.
Large tiles need a very flat floor, how flat is yours? Take a long straight edge or chalkline to calculate the "out of plane" in any 10 ft. length of the floor. Check many areas. The number you're looking for is no more than 1/4" out of plane in 10 ft. and 1/16" in 12". Actually for large tiles you would like within 1/8" in 10 ft. You may also want to consider using L.A.S.H. leveling or Tuscan leveling system to keep the tiles from drooping after you've set them.
Do some searching then come back with more questions.