So now onto the improvisation section. On the video I improvise a pretty simple solo over this part of the tune. The main things to think about are the time signature and the harmony/chord changes. For the first 8 bars we're improvising in 5/8 and all the chords are in the key of D#major. You can, therefore, simply take the route of playing D#major over the progression and use your ears to come up with lines and melodies you like. You may find that some of your usual licks take on a new lease of life over the 5/8 time feel! If you get stuck, try writing out some rhythms in 5/8 and using those to solo over the progression with the notes of a D#major scale. It can take quite a while to get used to phrasing in odd time signatures when improvising.
If you want to take a more targeted or chord specific (modal) approach then you should use the following scales,
A#7sus4 - A# mixolydian
G#Maj7 - G# lydian
D#add9/G - G Phrygian
Fm7 - F Dorian
Some people prefer this approach because, although all these scales contain the same notes as D# Major, it can enable you to outline the sound of each chord more clearly and directly when improvising. Simply choose the approach that works for you.
For the 2nd 8 bars we introduce a key new chord in the form of G#m6. For this chord I use a G# melodic minor scale. Incase you're not sure about this scale it contains the notes,
G#, A#, B, C#, D#, F (E#), G (E##).
Refer to infiniteguitar.com's lessons on major scale modes and melodic minor modes for more info!
Now onto the stabs section.