You answered your own question.
G sharp
F Sharp usually, but sometimes it can be G flat
G#
No. On a certain note with both a sharp and flat, (G, for example) they are the same distance from G, but going in diferent directions. G sharp raises the note by one half step while G flat lowers the note by one half step. However, it is possible for a sharp note to mean the same note as a flat note. For example, G sharp is the same note as A flat. This is called being enharmonic.
G#
Its a kind of note in music. Its also in the G-scale of g sharp it is on the grand staff on piano.
A flat. Because this note is between G and A, you can go up from G (make it a sharp) or down from A.
C sharp, D sharp, E natural, F sharp, G sharp, A natural, B sharp & C sharp We call the note C "B sharp" to avoid using the same letter name twice. If we used the note name "C" we would have 2 C-notes and no B-notes in the scale!
A
C sharp
no, g sharp is the only "landlocked" note, which means it can only be called g sharp or a flat, not any double sharps or double flats.
It becomes a double sharp. For example, F double sharp is the natural note G.