Half- sharp
Double sharp occurs when the location where a sharp or flat is supposed to be is covered by another sharp or flat. Lets say you wanted to play C but somehow B and C# were a part of the key. So on the...
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.
A double sharp raises the note one whole tone.
A double sharp is the enharmonic of B nature