First off all, D#7 has not the same notes as Gb6, here it gets tricky with stuff many people have never heard about

D#7 has the following notes; D# Fx A# C#, notice the Fx, the x stands for a double sharp and the musical sign fot that is an x with fatter ends but that is not on my keyboard but yes, double sharps and double flats exist.

Gb6 is made of the notes Gb Bb Db Eb or if you want it with sharps, F# A# C# and D#, so a regular F#.

as to your last question, the chord would be written with the flat 6 between parentheses like this; G (b6).

Hope this clarifies it

Herman