Can new grout be layered on top of old grout?
Yes new grout can be installed on old grout.  Make sure the old grout is thoroughly cleaned and then wet before installation.  I do this all the time.   There is absolutely no need to start over and given the quality of the install you have had so far I would say that starting over might introduce more issues.

On the pan you can expect a slight slope towards the drain but the pan should be flat to the foot.  Depending on what kind of pan he used your issues could be very severe or 1-2 hours of tile work.