Forget about "inquiring". You need to make an EC 261/2004 claim against IB for denied boarding compensation. The sole relevant facts are:
A. You were ticketed on IB flight XXX on XXX.
B. You were at the gate and ready to board at 35 minutes prior to scheduled departure.
C. You were denied boarding because IB had already offloaded you in favor of other passengers.

Therefore you are demanding EUR 250, plus hotel, plus food (for which you enclose receipts).

The rest of the back-and-forth is irrelevant and only causes problems and delays.

If IB denies your claim, you may then sue IB or forget it.