After I had read this whole thread, I wished the reason for my defective microphone would be a software bug. So I started looking for the bug(s) and did a factory reset. The first call after this action was successful. But only the first one. All the following calls brought the same problem: I can hear the other person perfectly but can’t be understood.
So I wanted to try it with CyanogenMod. @chrmhoffmann did great work and compiled CM11 for the FP1 - at the end of 2014. Unfortunately the rom file isn’t available anymore. Here the link to the suitable xda-topic and fairphone-topic.
But he is apparently working for another android version for the FP1 which already runs well and stable. Here the link.
Unfortunately this didn’t solve the problem of non-working microphone. So i ordered a new daughterboard at fairphone’s shop for 16€ (incl. shipping) and hope that will fix the problem…