Hi sashapiano,
The simplest octave fix is to simply play either note of the octave. The texture isn't as thick but so what and harmony is minimally changed.
In other double note situations (intervals), the right hand top note is often the melody and the bottom is usually either an inner voice or harmony note. The melody gets priority here and if a note were to be omitted it should be the non melody note or bottom note.
In left hand double note situations, the bottom note is the base (often the root) and the top note of the left hand is not as important and could be omitted but yes, use your ear.
As for adding/substituting notes, a knowledge of chords is essential.
Notes in a chord have a priority. The root (tonic) gets top billing. The name of the chord is the root. For example, in a C major chord, the root is the note C.
The 2nd most important note would be an E which is the 3rd of the chord C.
The most unimportant note which like Rodney Dangerfield gets no respect is the 5th of the chord which in this case is the note G of a C chord.
The ear fills in the missing notes.
In elementary method books a G7 chord is just 2 notes. G of course and the 7th F. These books leave out the 3rd B and the 5th D of the 4 note 7th chord.
At an ever so slightly higher level, G7 becomes a 3 note chord of G, B and F. The 5th note, D is omitted.
A chord chart would be invaluable to someone not fluent with them.
I hope I have been helpful, Joe.
P.S. Welcome to Pianostreet!