Hi,
I don't really fully understand this statement here
that with the crossbeams (each 4 m) at the front there is a deflection of 5-6 mm towards the middle now is
but in case you are asking whether your beams are allowed to sag 5-6 mm in the middle over 4 m length:
Yes, they are allowed. Steel construction is usually designed with L/200, meaning under load the beams may deflect by length/200 = here 20 mm.
If you want less deflection, the necessary cross-section (and thus the price) of the beams increases significantly.
However, water should not actually stand at any transition points. That is a source of constant rot and trouble.
Best regards,
Andreas