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So Kaz, now I got these 2 huge vectors with the FFT's scaled real and imaginary data in. Now I have to Pythagoras them, right? But as what kind of format do I have to look at them?
Is it now an signed integer?
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yes once you do the scaling the values are signed 2's complement as input.
The output practically should not be that wide and you will need to observe the exponent as to what range is practical for your case then do some trimming on bits to fit fewer bits. You don't need to square it up to amplitude, you might just check each of real and imaginary directly.
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