Cracked subway tile on shower cub after remodel: what's my next steps
I am a license tile installer of 35 years and you definitely have a leak in your pan and/or non existent pan on the curb.  The reason the grout is cracking and tiles are pushing away from each other is because the curb was built with wood ( wood swells when I gets wet) this is not the proper way install this, and soon it will develop mold - if it hasn't already. Curbs must be built with concrete blocks (filled solid) or a form builder utilizing concrete (dry pack).

This issue needs to be addressed as soon as possible, that curb can channel water into your adjacent walls as well creating a much larger issue. 

To find out if the pan is leaking, as Chris stated above, remove the drain cap, plug the drain ( must be water tight!) First, mark a tile with a fill line using a crayon then fill up the pan to your mark. I would put it slightly below the level of the curb. Wait 48 hours to see how much the water has dropped below the line. Typically a small amount for evaporation, maybe the thickness of your crayon line can be accounted for, anything more than that you have a leak in the pan and it will need to be replaced.  Unfortunately in either situation your glass will need to be removed from the curb.