1) His pipework isn't perfect by any stretch of the imagination - you will need a qualified plumber to report on that
2) You don't drop waste pipes into notched joists, you just don't, they are far too big - again that should form part of the plumbers report
3) When the joists are like regardless of whether he did it on not, you don't put a shower or anything else of weight on it and expect it to support - you will need a joiner to report on that, he will be able to comment on whether the cuts are new or not.
4) Structurally you'll need a engineer to report on what needs to happen re the joists.
Also re @Bodd comments there certainly looks like the 2 joists on the left (where the grey waste pipe comes to) may have already have old cuts on the end you can see, but not sure about the reverse end but all the joists to the right seem to have new cuts. Need a proper close up (on site) view of it all.
You really need to get the floor up and get things properly inspected, once that's done you will be in a better position to know how to take things forward.
2) You don't drop waste pipes into notched joists, you just don't, they are far too big - again that should form part of the plumbers report
3) When the joists are like regardless of whether he did it on not, you don't put a shower or anything else of weight on it and expect it to support - you will need a joiner to report on that, he will be able to comment on whether the cuts are new or not.
4) Structurally you'll need a engineer to report on what needs to happen re the joists.
Also re @Bodd comments there certainly looks like the 2 joists on the left (where the grey waste pipe comes to) may have already have old cuts on the end you can see, but not sure about the reverse end but all the joists to the right seem to have new cuts. Need a proper close up (on site) view of it all.
You really need to get the floor up and get things properly inspected, once that's done you will be in a better position to know how to take things forward.