Power outage in one room
What you just described are backstab connections and that kind of failure is typical with them.   

The exposed wire you saw isn't good, but it may have just been a matter of the insulation being stripped too far back.  It's also possible they cut the insulation correctly then didn't jab it in far enough.  Regardless, backstabs are a low quality way to make that connection, and will tend to do this even if done by the book.  

Your problems will be cured by switching to either side-screw connections already on the socket, or the "screw-to-clamp" type connections used by Leviton.  Those Prograde outlets cost $3.  Any competent handyman who owns a torque screwdriver can handle this task, so hit Taskrabbit or Craigslist.  

Also have the handyman check the wire and compare it to the breaker. The breaker rating must match the wire capacity, sometimes fools  change the breaker to too large a value, risking a fire.  The fact that the wire was in backstabs means it is almost certainly 14 AWG, which means it should be a 15A breaker. 

All that, however, does not take you "off the hook" for overloading the circuit.  I suggest getting a Kill-a-Watt power measurement device and find out what your devices draw. Most of the things on your list (together) don't worry me, but PCs can be a real wildcard. A gaming PC with a top video card can absolutely push that circuit over the edge.