Are there any cockpit indications when an engine has separated from the aircraft?
This is the indicator that shows you when one engine falls off in a multi-engine aircraft:



If the right engine falls, off, the little ball will move left. If the left engine falls off, the little ball moves right. 

If you only have one engine, or both engines fall off, you need to use a different indicator that looks like this:



if both engines fall off, this white pointer will start to move towards the "40", and you might hear an alarm, a voice shouting "stall, stall", or feel the stick shake.

if you have one engine and it falls off, the white pointer will move, but in an indeterminate direction.