You can install an interior weeping system similar to what you would normally do on the outside, but without the waterproofing.
Start by jackhammering out about two feet of floor around the edges of your garage, as close to the walls as you can get. Dig down until you reach dirt, and if that's not at least two feet down, keep going. Now, put down a couple inches of 3/4" crushed gravel, and then install weeping tile (it's not tile anymore; it's 4-6" corrugated plastic drain pipe with a nylon mesh sock over it). Make sure the sock is continuous across any joins you make in the weeping tile for corners etc. This is a good time to direct those drain holes down into this trench, where the water they drain will flow into the weeping tile. You'll also need a sump, or a connection to a downhill storm sewer; direct the weeping tile to this sump pit or the storm drain. While you're doing all this a center drain can't hurt too much; you can tie it into the weeper wherever it's convenient, just make sure the garage floor and the drain flange are level, or that the garage floor slopes slightly to the drain.
Now, you can install waterproof sheathing on the interior walls contacting the concrete. Normally this product is designed to go outside the foundation walls, but in cases where that's infeasible it can work this way too. The idea is to trap moisture that weeps through the wall behind the sheathing, where it will then be directed down the wall and under the slab to the weeper. So, you'll install the sheathing, which should have an air space between wall and most of the layer, and make sure the end is down in the trench by the weeper.
Backfill the rest of the trench with 3/4" crushed gravel up to the slab footing, then patch the slab with new concrete. Your garage should stay much drier.
Visit your local tool rental store. They will have something that will make this much easier. There is pneumatic scrapers and concrete grinders
For the hardwood laminate you dont not need to even remove the old tile but to lay ceramic tile you should
Best Answer
The slab upon which the addition is to be built should normally be level and without a slope to it - (a garage floor may be different). In addition the final grading of any surrounding dirt coming up to the slab/foundation should be BELOW the slab level and should slope away and down as it gets farther from the edge of the new house line.
The contractor that placed the slab is probably the wrong person to be getting assurances from regarding whether the non-level slab is OK. If they messed up the slab they are probably going to try to convince you that it is OK and try to proceed to build on top of it!! Get a formal opinion from 3rd party or your building inspector.
During the construction phase a new addition slab that is built up even with an existing floor line is likely to be susceptible to rain water coming in under the existing wall base plates even when the slab would be level. A good contractor would probably make allowances to place plastic up on the existing outside walls that drapes down over the new slab and out some 6 to 10 feet to help keep rain water from collecting up near the place where the new slab joins up against the existing wall area. If your slab with it's slope toward the existing house is a legitimate design then it seems to me that such temporary measure may be even more important. However I suspect that the slope is completely improper in this case for a bedroom addition and the fact that the contractor did not take steps to keep rain water from running into your house speaks volumes about the poor quality of the workmanship being done on your project.