The combination of the first C & D (4th and 5th) waveforms makes no sense. Either the oscilloscope has an offset error, or the output offset is changing when you connect the oscilloscope probe. In the latter case, it's most likely a case of high-frequent self oscillations, see my previous post #8. Also the distorted output waveform suggests an oscillation or other serious hardware problem.
My suggestion is to try a user friendly 10 to 20 MHz GBW OP in your circuit.