Id use SLC for a couple of reasons.
One, it protects the mat form my big feet and tools while tiling.
Two, it leaves a good surface to tile off.
Three, Any air voids around the mat, below the tiles will act as an insulator and reduse the thermal transfer of heat to the tile. In the worst case of the cheeper wires they can burn out as they heat up too much with just air around them.
Agreed with Grumpy, always try and install 10mm dense insulation boards, can be up to £20 a m2 but the tiles will be warm after 20 min as opposed to 3 hrs. Long term savings.
No
tiler worth their salt should be using dot and dab, very poor show indeed.
I would ask them to explain their tile fixing methods and any concerns you have about them as early as possible. As they are finished, or nearly finished I would let it go and see how the job turns out, ie boast tiles, efficiency of the heating. They should have liability insurance that should cover UFH and that might be the way to go if things are not to your satisfaction.