A key signature with one sharp (F#) would be either G major or E minor.
The G-major scale has only one sharp (which is F#)
G Major has one sharp, which is F sharp.
The F-sharp natural minor scale consists of these notes:F-sharp, G-sharp, A,G,C-sharp,D, and EThe F-sharp harmonic minor scale consists of these notes:F-sharp, G-sharp, A, B, C-sharp, D and E-sharp.The F-sharp melodic minor scale consists of these notes:[going up] F-sharp, G-sharp, A, B, C-sharp, D-sharp and E-sharp.[going down] F-sharp, E, D, C-sharp, B, A and G-sharp.
The mediant of any major scale is the note that is a third above the tonic (root) of the scale. In the key of F sharp major, the tonic is F sharp, so the mediant would be A sharp.
Just one, and that would be F sharp.
The natural minor scale with the most sharp notes is E natural minor, which has one sharp note (F#).
The G-major scale has only one sharp (which is F#)
G Major has one sharp, which is F sharp.
E to F-sharp is one whole step. F-sharp is a major 3rd above D, so it's part of the D major scale.
The F-sharp natural minor scale consists of these notes:F-sharp, G-sharp, A,G,C-sharp,D, and EThe F-sharp harmonic minor scale consists of these notes:F-sharp, G-sharp, A, B, C-sharp, D and E-sharp.The F-sharp melodic minor scale consists of these notes:[going up] F-sharp, G-sharp, A, B, C-sharp, D-sharp and E-sharp.[going down] F-sharp, E, D, C-sharp, B, A and G-sharp.
In theory it is impossible for a scale to have but a flat and a sharp but if it is in inharmonics then yes it is possible to have a flat and a sharp just depends on how you look at it.
The mediant of any major scale is the note that is a third above the tonic (root) of the scale. In the key of F sharp major, the tonic is F sharp, so the mediant would be A sharp.
Just one, and that would be F sharp.
An E natural minor scale is written with a one-sharp key signature, so you just write out the scale in semibreves and add an additional D sharp for the harmonic minor, and two additional sharps to the sixth and seventh degrees when ascending in the melodic minor (C sharp and D sharp). You lower the sharps and revert back to the natural minor when you descend through the scale.
The subdominate refers to the fourth note of the scale ( assuming it is a diatonic scale). In this case the subdominate of the C sharp major scale would be F#.
F sharp C sharp G sharp D sharp
Only one: the F-sharp.