B flat
It's called enharmonic spelling. An example is C-sharp and D-flat.
A double sharp is the enharmonic of B nature
A flat. Because this note is between G and A, you can go up from G (make it a sharp) or down from A.
F sharp is the enharmonic.
F sharp is the enharmonic.
The enharmonic of E-sharp is F-natural.
The enharmonic tone for F is E sharp.
Being that it's a whole-step away from another sharp or flat note in both directions, there is no possible double-sharp/flat spelling for it.
B flat
A sharp
A sharp.
The enharmonic equivalent to A-flat is G-sharp; The enharmonic equivalent to G-flat is F-sharp.