I have a simply supported frame.
When i run the model as a simply supported frame, i am seeing normalforces as i would expect.

I want to add beams under my deck, but whenever i add a shell, and a designelement to represent the beam, i am seeing huge normal forces. Is this the force pairs from the moment i am seeing, or how is this happening?

Normalforce plot without beam (local y is running along the length of the deck)

But shouldnt sofistik compensate for that, integration of the normalforces over the tbeam should be equal to zero?

I did read chapter 2.3.4 in the ASE manual, and also read about TBEX in ASE manual.
To me, it doesnt make sense why SOFiSTiK/WinGraf would show me the normalforces AND the moment.
Since the normalforces occur because of the forcepairs from the moment force?

because the normalforce occurs from the moment. So either you design for the moment or the normalforce, but not both at the same time.

Lets say for example, i have a normalforce in my deck, for example 100 kN tension, and 50 kNm momentforce.

Now i design a beam under my deck - my normalforce is now way higher. To get the correct normalforce, i would have to integrate normalforces over my t-beam, before i have my “real” normalforce, and can do a proper design calculation.
Am i wrong in assuming that?

Yes, for design purpose you have to integrate forces, then you take this integral (MY, and N~=0) to design sections, provide reinforcement etc. However integrating forces for design does not vanish forces from slab.

You have a shell-modell with excentric beams/material, there are physically correct (internal) normal forces from bending. And there are also in reality this normal stresses in the shell-elements.
Usually, however, slabs and slab beams are simply dimensioned with the pure bending moments without directly considering the force components tension/compression (except for the slab connection reinforcement).
Further details can you see in ASE-manual, 2.3.4 (T-beam-philosophy).