Concrete – How to remove or level grooves in thinset mortar from a concrete slab

I had something similar in my basement - a drain in the middle of the floor, and the floor around it sloped toward the drain.

We did pretty much what you described and it turned out really well

1. Clean the floor up nice.
2. Used a wire brush to roughen up the surface a bit so the new concrete will adhere well.
3. Poured in regular concrete to almost level it out.
4. Used thin-set mortar to finish it off (the same mortar you would use for setting tiles)

As for your sagging beam - they make special house jacks for that kind of stuff, but a hydraulic car jack with a 4x4 would probably do the trick as well (for your situation anyways).

Grinding concrete is a very dirty job. If I had to do it I would use a 9 or 4 1/2 inch grinder with a concrete grinding wheel. At least an N95 dust mask, goggles, preferably like motorcycle riders use with the foam around the edges to keep dust out. I would put one or two shop vacuum cleaners hoses in the exhaust vent to create an air flow through the bathroom. You will need to mark where the toilet base hits and remove the toilet then grind away free hand. Leave the outside edges till last so you can put a straight edge across to measure progress. Leave the area where the toilet sits high, it wont be noticible when the tiles are in. Can you get the plumber to fix it, he screwed it up. For the vacuum cleaner's you could remove the door and make a plastic door then you could just run the hoses under the plastic and let air be pulled in from the vent, try and have a slightly negative pressure to keep the dust in the bathroom.