I'd be pretty sure that your symptoms indicate that your rear pads are worn down to the metal backing plates, which probably means your rotors are going to be damaged. You may be able to get them machined if they are still within rotor thickness tolerance, but given the shimmy they probably are toast. DIY for sure, it's nothing that requires special tools or specialist knowledge. Plenty of help in this and other sites see http://www.bmwe34.net/e34main/mainte...rakes/pads.htm and http://www.bmwe34.net/e34main/mainte...kes/rotors.htm. Good luck!
June 88 535iA, 173,000 km; Sep 00 735i 170,000 km