I have read through all of this and tried to make my opinion as objective as possible....YES the floor could've been tricky once he started, YES cheap tiles can bow, and the differential already mentioned would suggest this as a possibility....but the standard of the finished floor is miles away from being to an acceptable standard (this doesn't help you much at this stage I know!) and the state of the grouting is amateurish at best, and I mean at best! Throw into the mix tiles with 3 breaks in them.....there is no where to hide for our man.
Are we allowed to ask who the culprit it or have i missed that bit?
Your first port of call should be to get clear and concise advise on what your rights are and I would do it ASAP just in case there is any potential to miss things due to time line etc
You should also trawl through texts and emails to see what you can pick out from him that may help at this stage.
I am sure we have all opted for the cheaper option at some point in our lives, but you have been well and truly let down by this plank.