In the picture below, it looks like there is a rest superimposed on top of a note. What does this mean?
It's a misprint. Both are 16th-note
As, and the rests are misplaced.
The rests should be placed lower on the page, level with the stems-down eighth note chords. They represent a separate "voice" — imagine two instruments playing: one instrument plays the upper notes, the other instrument has the rests and the lower notes.
Whatever this piece is, I highly recommend looking for a different version. This is very poorly engraved. In addition to the misplaced rests, the final note either should be an eighth note (not a sixteenth) or should not be dotted.