I am using the same camera as you with a 1050mm Klevtsov-Cassegrain and a 0.5x reducer. I think that's quite similar to yours. Vignetting is very visible indeed but is also corrected 100% with flats. This is the price of using a reducer, yes it is reduced if you remove it but then you are working with a slower telescope at a much larger focal length so you have completely different field of view, tolerance to tracking errors, required exposure times and so on.
How do you place the reducer? For me it is camera+T to 1.25" adapter + reducer. That gives a 45mm distance between the sensor and the reducer which is not ideal as the recommended distance is 55mm. This has the effect of smaller reduction (effective focal length becomes 623mm instead of 525) and some aberrations at the edges. I have decided life is too short to worry about that missing 1cm. But vignetting is the one thing I do not care about at all since flats take very good care of it.
To answer your second question I don't think 4/3 sensors have any particular problem with reducers. If anything, the smaller sensor is less prone to any kind of optical issue because it is at the center of the image circle. If you plug a DSLR instead you will probably be horrified at the extent of vignetting and other aberrations outside the central 1/3rd of the image or so

Cheers,
Dimitris