E-sharp is the same as F-natural.
To play a sharp B flat on a trumpet, you would use the first valve and the third valve together.
On a standard Bb trumpet, the fingering for C is open.
On a standard Bb trumpet, the fingering for A is 1st and 2nd valve.
On a standard Bb trumpet, the fingering for F is 1.
On a standard Bb trumpet, the fingering for Ab is 23.
On a standard Bb trumpet the fingering for a high G is open. An alternate fingering is 13.
On a standard Bb trumpet, the fingering for low G is 13 and the fingering for higher Gs is open.
d sharp right above middle C is the same as Eb -- 2/3; the D sharp above that is 2.
A double-sharped note is just raised two half-steps from the original note. So if you have A##, the first sharp would go to A#, which is the same as B-flat, and the second sharp would be the A##, which is the same as B-natural.
no fingers
On a standard Bb Trumpet, the fingering for a low Eb is 23 and the fingering for higher Ebs is 2.