1985 BMW 535i Car makes a thump when the clutch is released

Drive Train Axles Bearings problem
1985 BMW 535i 6 cyl Two Wheel Drive Manual 200K miles

When changing gears if the clutch is released quikly there is a loud thump in the rear of the car. If I release the cluthc smoothly no sound. My question is. Would this be drive shaft related or axle related? And how do I check which is bad? Second problem is the car idles fine at 800 rpms; however, when the accelerator is pressed the car chokes out. I have replaced the fuel filter but no change. Is there anyay to determine which pump or relay is bad? Also, the fuel issue is spordic.