You can put the M3 rear subframe in, but you need to get a shorted drive shaft. That will cost some money to get it balanced properly.
If you keep the 135i rear brakes you will need adjustable rear toe links to get the correct wheel alignment, as the 135i hub carries are slightly different to the M3 ones. See the details of another installation
here. I don't know about using the M3 rear brakes. I guess it may be ok if the piston size is similar.