How long have you owned the car, and when was the last time the brake lines were flushed?
Based on your description of the rear brakes I would assume the brake fluid has been allowed to age to the point where it has absorbed quite a bit of water. This leads to corrosion that had likely led to the ruin of the calipers.
The rear brakes sound like they are frozen, and the front brakes sound like the caliper to piston seals are shot. The lack of evidence that the rear brake pads are contacting the discs suggests the pistons are frozen in the calipers and do not move, while the failure of the front pads to withdraw slightly when you take your foot off the brake is a sure sign the seals are shot. In either case the best way to solve the problem definitively is to replace the damaged caliper. This is especially recommended for the front ones. Brakes tend to be pretty rugged, and I have unlocked frozen pistons with brute force before, with success. But I am not sure I would do it again.
I do not recommend you buy rebuilt calipers as the caliper rebuilding process requires a certain precision that is not always met (honing to clean up the bore of the caliper makes the inside diameter larger while any cleaning up of the piston makes it smaller and those two effects combine to ruin the seal preload), and the same problem can arise again (the "sticking" brake).
Good luck, Jim
1986 Euro 190E 2.3-16 (291,000 miles),
1998 E300D TurboDiesel, 231,000 miles -purchased with 45,000,
1988 300E 5-speed 252,000 miles,
1983 240D 4-speed, purchased w/136,000, now with 222,000 miles.
2009 ML320CDI Bluetec, 89,000 miles
1971 220D (250,000 miles plus, sold to father-in-law),
1975 240D (245,000 miles - died of body rot),
1991 350SD (176,560 miles, weakest Benz I have owned),
1999 C230 Sport (45,400 miles),
1982 240D (321,000 miles, put to sleep)