I am having difficulty "understanding" mechanical energy. My question, is
mechanical energy conserved in real situations?
Your assistance is greatly appreciated.
As is frequently the case, the answer is, "it depends".
Your question includes the word real, as in "real situations". There are systems in which the departure from conservative is so small that for all practical purposes mechanical energy is conserved. For example in the motion of the Earth in its orbit about the sun, the sum of kinetic and potential energy changes so slowly that in centuries of observation the orbit has remained stable. Eventually though, the loss of energy through tidal friction, meteorite collisions and so on, will result in orbital changes.
If by real you mean observable on a human scale and limited in time to a few human generations, there are real situations in which mechanical energy is conserved. If we further restrict the time scale then there are many other systems that appear to be conservative. The vibration of a guitar string over a single cycle may be treated as conservative, even though in a few seconds the motion will decay away as sound energy is radiated away and heating of the string takes place.
If by real you mean systems that are observable on a human scale but are to be observed forever, there are no real situations in which mechanical energy is conserved. If we give up the "observable on a human scale" restriction there are some real situations that last as long as the system lasts where the sum of kinetic and potential energy remains constant. The motion of an electron in its orbit about the nucleus of a hydrogen atom is an example.