I'm having trouble learning Moonlight Sonata without a piano teacher. What does a natural notation and a sharp symbol mean in front of the f, which is already sharp in the key signature?
I can't find it in the edition I'm looking at, but probably this is a courtesy accidental to make it easier to remember what note you're playing.
Strictly speaking, courtesy accidentals aren't needed for any theory reason, but they can make a difference when playing. Usually they are found at the start of a measure canceling the accidental in the previous measure. They are up to the editor since they don't affect the playing of the music, and vary between editions.
In c♯ minor, fx is the leading tone to the dominant (g♯), so it occurs pretty frequently. To remind you when you're looking at a "regular" f♯ after a passage of fxs, you could see a natural and then a sharp.
It means that you are going from a double sharp to a sharp.
In classical notation for instance when you write a melodic minor scale with a double sharp going up and just a regular sharp going down you use a natural sign followed by a sharp to indicate the E## is going back to a E#.