I guess you should go for completely new foundation, so that you don't need to spend on the maintenance of later. Also, you will not be having any issue with the building regularity body.
BeefCube, I think you are right this one is the perfect solution to fill this concrete slabs gap. Just let us know the outcome once you finish the task. Hope you will be successful.
According to me, you will not be having any problem converting garage into utility room. I guess you should go ahead with this modification without any worry.
I guess you can search the internet for such services in your area. I am sure, you will be getting many contacts providing such services. Contact them and select one who gives you the best deal. Make sure you check their previous work before doing so.
Apart from above, you can also order...
According to me, you have tried 3 times to get useful DIY tips, but was not successful. I will advise you to take professional person advice to get your leakage problem sorted quickly.
After reviewing you condition its seems that removing 25 mm seems to be only better option for you. I suggest you to agree with your builder point of removing 25 mm of screed.
I will advise you to get completely new flooring. If you go for some sort of repairs. It will not stay for a long time and again, you need to spend on repairs. If you are planning for longtime renovation, its better to have completely new renovation.