BMW E28 brakes shudder or judder when braking

The most common cause is a warped brake disc. The shudder can also come from a worn bushing that pumps when braking. Check the hub runout and the caliper sliding parts before replacing the discs.

Yes, the recommendation is to replace both at the same time and to check the calipers at the same time. That way the new discs do not wear faster than the old ones. A ventilated disc does not fit a non-ventilated caliper.

If the discs and calipers are the same on both sides, the cause may be torn control arm bushings. Squealing can be caused by a glazed disc, for example because of grease. Remove the wheel and inspect the disc and the other brakes.