#1 it looks like the frame was installed wrong. It should have been installed so the seal on the bottom of the door would end up being on top of or on the other side of the threshold.
Right now all the waters running down the door and landing on the wrong side of the threshold and running out.
There's also no siliclone around the side frame bases.
The threshold looks pretty flat, there should be a taper back to the shower pan. Also the threshold tile is pieced and there appears to be a grout line right at the door frame this looks to be acting like a little dam. it is really best to have a solid piece on the top of the threshold and tapered back to the pan then you should be in good shape. So try to find a solid white marble or other solid surface threshold, tear off the tile and install the marble with proper pitch 1/4 per foot minimum. Or buy yourself a new door that has an integral waterproof threshold that could be installed over the existing tile.