I don't understand what the issue is. As they replied, probe compensation is only implemented in 10X mode. So, the adjustment capacitor will not do anything. This is not a defect, this is how probes work.
Just use 10X mode and forget that 1X exists, it is not useful in most day to day tasks.
No, it is not 34 MHz, it is an error in measurement based on the incomplete data. You need to adjust the time scale so that a few periods are visible. There is no way to measure a "frequency" of a simple edge transition.