Altimeter adjustment
Whilst adjusting the baro-scale knob from the front access hole may sort a QFE indication error, it may in fact be that the altimeter is out of calibration across it's range and you can't check this without a calibrated pitot-static test set. There are AD's in force covering quite a few common GA altimeters for mis-reading when the baro-adjustment has come un-done. Best to let a qualified instrument shop such as Aircraft Instruments at Breighton or Pandect at Wycombe sort it out.
For the transponder, it may get it's altitude from either an encoding altimeter or a blind encoder. In either case, the output is always referenced to 1013mB, so your altimeter baro setting will have no effect on the transmitted data. Again, calibration requires checking bottom and top of the operating range, so you need a calibrated pitot-static test set and a transponder test set, ensuring of course that you don't transmit above-ground altitudes where they could be picked up by TCAS-equipped aircraft or they could get false TCAS alerts. If you have a Mode S unit, ensure it's in GND mode when doing any testing.