E Natural
Remember, double sharp takes two half steps!
First you begin with D natural. Since double sharp represents two half steps (above) you would then move one half step (next key) which is D sharp then you would take the next and final half step which lands you in E natural.
E natural and D double sharp share the same pitch but but are represented by different letter names or accidentals
D-flat
It's not equivalent to any sharp, but it is equivalent to D double sharp.
The enharmonic equivalent of C minor is B-sharp minor. Enharmonically, C minor and B-sharp minor sound the same but are written differently in musical notation. C minor consists of the notes C, D, E♭, F, G, A♭, and B♭, while B-sharp minor consists of the notes B♯, C♯, D, E, F♯, G, and A.
The position for D sharp on a piano is the black key immediately to the right of the D note. On a guitar, it can be played by pressing down on the 1st fret of the second (A) string or the 11th fret of the fifth (A) string. In the context of music theory, D sharp is the enharmonic equivalent of E flat, meaning they are the same pitch but have different names based on musical context.
B sharp, C double-sharp, D double-sharp, E sharp, F double-sharp, G double-sharp, A double-sharp, B sharp.
E natural
"Flat" means to go down one semitone. Look at a piano (or similar) keyboard, and check what you have one to the left of "C". Since on a piano there is no black key between "B" and "C", the next semitone down from "C" is simply "B".
D-flat
Do you mean the note? An enharmonic of D sharp is E flat.
D sharp minor
E Flat Minor
D-flat major. It's the enharmonic equivalent.
F# minor is the enharmonic equivalent of G♭ minor, which is the subdominant key of D♭ minor. D♭ minor is a theoretical key with a troublesome B double-flat in its key signature. This is why you would usually see the key orientation of a song or passage with tonal center of D♭ notated around its enharmonic equivalent, C#.
The enharmonic of a note is another note that sounds the same, so the enharmonic of d flat would be c sharp.
D
It's not equivalent to any sharp, but it is equivalent to D double sharp.
notes that are called different but have the same fingerings. Examples: c# and b natural. This idea is useful when, for example, a composer is in the process of writing harmony for music that is moving from one key to another.