e major
You would be either in the key of F or D minor. Impossible to say which one without knowing the chord progression or the melody; does the Dm or the F feel more like "home"? You could modulate to any key you like, but you're be more likely to modulate to a "close" key. Since F or D minor have one flat, the close keys would be those with two flats (Bb or G minor) or no flats (C or A minor). Most likely, you'd go to the dominant key, which would be C or A minor (depending on whether your tonic key was F or D minor).
Firstly, there is no B minor chord in the key of F sharp minor. Rather, it is A sharp minor chord. And you can use any chord at the end of a chord progression. Why not!
A major, or F# minor
B Major and G sharp minor. The sharps are F, C, G, D, and A sharp, in that order.
The key of E major and its relative minor, c sharp minor, both have four sharps. Additionally, key signatures apply to all music not just the piano and remain the same regardless of instrument. When referring to the piano the term "key" usually refers to on of the actual white or black keys that are pressed down to make a sound of the corresponding pitch. Each key on the piano is attached to a hammer that hits a string inside the instrument, thus the piano's classification as a percussion instrument. The strings are of different lengths and thicknesses, creating the different pitches. Each key on the piano is responsible for one pitch. Therefore a single key on the piano cannot "have four sharps", as you asked.
E sharp minor
The key of E minor has one sharp: F sharp. It is the relative minor of G Major.
D sharp minor
Four key signatures have G sharp and E sharp in them: F sharp Major, D sharp minor, C sharp Major and A sharp minor.
You would be either in the key of F or D minor. Impossible to say which one without knowing the chord progression or the melody; does the Dm or the F feel more like "home"? You could modulate to any key you like, but you're be more likely to modulate to a "close" key. Since F or D minor have one flat, the close keys would be those with two flats (Bb or G minor) or no flats (C or A minor). Most likely, you'd go to the dominant key, which would be C or A minor (depending on whether your tonic key was F or D minor).
The parallel minor of F-sharp major is F-sharp minor. A parallel minor key is the one with the same tonic note.
That would be the key of A-sharp minor, the relative to C-sharp major, which contains seven sharps. The leading tone is G-double-sharp.
The minor key with 1 sharp is B minor. In the key of B minor, the F# is the raised seventh degree, which is characteristic of the harmonic minor scale. This key signature gives B minor its distinctive sound, often associated with a somber or melancholic mood.
G Major or e minor. The sharp would be F sharp.
Firstly, there is no B minor chord in the key of F sharp minor. Rather, it is A sharp minor chord. And you can use any chord at the end of a chord progression. Why not!
The key with 6 flats is G flat major (this is the same as the key with 6 sharps: F sharp major). The relative minor is e flat minor (also called d sharp minor).
Remove the 4 sharps and add 1 flat. Raise it up a minor 2nd.