Yes that’s right, the second one will be # as well because it’s noted as a # previously in the same bar.
The reason for a G# in this song is because the song is in the key of A minor, and so G# is the leading tone in this key.
That means it’s the note just before the root note which is A. The leading tone always creates the biggest resolution in music because it wants to resolve to the tonic, which is the “home” key.