Differential high voltage measurement using a transformer
Assuming you have your transformer HV side to the circuit, 6v side to the scope ...

1) The current conducted via C1 should not cause a danger to the earthed scope. It is likely to add spikes to your readings. You can get mains transformers with an interwinding screen, designed to shield C1. Connect the screen to the scope ground, all the C1 current will flow into there, and none will turn up in the 6v winding.

2) R2 C2 will reduce the differential mode bandwidth, which is not necessary (see later).

3) R4 R5 will reduce the loading on the circuit, but are probably unnecessary. If the mains side is to the circuit under test, then there should be little need to use R4 and R5, as the impedance will be relatively high. A series capacitor might be useful for AC coupling, because although the AC impedance is high, the DC resistance is low, and the ability to make a measurement in the presence of the DC bias is useful.

An ordinary mains transformer is built on an iron core that's engineered to be low(ish) loss at mains frequencies, and very little more, that is, as cheap as possible. The frequency response / waveform fidelity may well be inadequate for components above mains frequency. Those sharp edges you mention will almost certainly not be visible, at least not in their original shape or amplitude.

People do use transformers to measure in the way you've drawn, but they tend to be ferrite or air-cored, if they are going for any real bandwidth.