What does the horizontal lightning bolt over the C sharp mean? Also, what do the double grace notes (the two semiquavers joined by a beam) mean?
It's an upper or inverted mordent. Play C#, the next note up in the key/scale, then C# again, all squashed into when the C# would be played normally.
The 'double grace note' is pretty well the same thing, just written out as played. I guess the tune's in A major, so why the F is sharpened, - don't know. Maybe it's in A minor, and modulated, rather than change the key sig., the composer used accidentals.