Problem 1: I have a 1986 740 GLE wagon and the other day it had trouble idling. When I turn it on the car jumps back and forth from 800 rpm to 500 rpm. When I put the car in gear it struggles to keep the engine going and requires assistance from me to not stall. This usually only happens when it’s cold. Problem 2: When I go above 60 mph the car shakes violently but when I go below 60 it drives normally.

 

violent shaking usually is caused by a bent wheel

your idling problem could be a lot of things.... there's a microswitch in the throttle body that tells the ECU the throttle is at idle, and when it is, the ECU monitors engine RPM and pulses the IAC (Idle Air Controller) to maintain a suitable idle. with the IAC disconnected, and all loads turned off, in neutral or park, a warmed up engine /should/ idle about 500-ish, the IAC brings it up to 700-750,a nd maintains it there whether its in gear or not.

cold, the engine should idle at about 1000 rpm

things that can mess this up...
1) something was fubar, and someone messed with the idle settings on the throttle
2) the IAC is gummed up
3) the idle throttle position switch is flakey or non-functional
4) excessive air leaks, especially the rubber hoses to the IAC
5) .... something I didn't think of....

 

If I were you i would immediately check your ball joints on both sides.

 

i checked the ball joints and they are completely shot

 

glad you could find out before something really bad happened at speed...