How to diagnose problems with wall
Very much NOT an expert here, but in your shoes I think my first calls would be to my homeowners insurance and the council. Find out who did the work, and if it could have caused the problems. Finding out what permits were filed might help.
Again, not an expert, but if the lifting tiles and cracked grout are in the shower they are going to need to be repaired sooner rather than later. If there is not already water damage, there will be.
I would make the phone calls first, but if you want to start repairs I would suggest taking plenty of pictures before pulling anything down. Actually, it wouldn't be a bad idea to take plenty of pictures (before, during, and after repairs) no matter what decisions are made or who does the work.
You might also consider keeping a little notebook. Jot down any conversations or phone calls on the matter. Who you talked to, when, and what was said. It's a good idea to document everything unless you're OK with paying for all of the repairs yourself.