Floor slab inside or outside the insulation

As far as I know, 10-15cm of insulation is also planned under the slab, then the "normal" insulation on the slab for underfloor heating or yes, under the screed. The basement is also insulated from the outside - then the overall construction fits again.

AFAIK, the insulated base slab below is still the exception (to my knowledge, the required insulation boards are somewhat more expensive).

The insulation underneath leads to fewer thermal bridges. When the base slab is insulated, the (interior) walls create thermal bridges (which can be reduced using special cove stones).

With underfloor heating, i.e. heated screeds, insulation should be placed between the heated screed and the base slab in both cases (as well as with the floor ceiling).

The reasons cited in #1 are both insufficient in my opinion. They are rather weak, if not outright incorrect statements.

I would probably go by how the contractor always builds. Because he can do that

Without having a specific opinion on this question, I would generally recommend this: whenever there is a justified suspicion that two construction methods are equivalent, take the one that the executor masters perfectly. Differences between system X and system Y are often marginal, whereas the factor "freedom from defects" (which becomes significantly more likely through experience) is a major advantage. In the worst case, the executor thinks imperfectly and uses a material or laying method that is (unfortunately: only) correct for X, but then applies it to Y.