How to repair the two sloping concrete slabs

I’m guessing that slab is on the ground floor .If so, and then from my experience it is much cheaper and easier to make a new than to fix the old slab. Firstly, you should smash the old one and then check groundwork under the slab. If it is not quality (well compacted) then you should pour some Breakstone, gravel and compact it as much as possible. Then you can work on a slab. It should be at least 15cm thick (round 6 inches if you are in US) and make sure that you use reinforcement; you can use either bars or net. At this stage you must make a decision if you want to make a slab „floating“ meaning separated from the walls, or you should place some steel bars from the foundations of the walls to the slab. This way they would be connected, act as a moonlit structure. But unless you have a problem with underground water, or anything that could cause negative pressure maybe you can go with „floating“ slab; in which case you should use something to separate slab from the walls while you are casting concrete, something like very thin Styrofoam placed on the walls.

If you want to do radiant infloor heating you will need to insulate under the slab. If you don't you will constantly be rejecting heat to the ground underneath the slab, and it will suck excess heat out of the system. If your not going to insulate beneath the slab, abandon the idea of radiant infloor.

Your also going to have to use HE Pex for radiant infloor. Standard waterline Pex is not allowed for hydronic heating systems.