#1
I feel like an idiot having to ask this but what is the correct name for this tuning
Eb Ab Db Gb Bb eb and my other question when tuned like this do you have to shift the positions of scales?
#3
This is a completely normal thing to wonder about, and everyone wondered about it before someone told them. There is no "name" its just "tuned down to Eb" and yes you have to shift the scales down. For more info use the search bar or go to the lessons section and go to "Learning Music Theory: The Beginning"
#4
Eb standard, or 1/2 step down.

As far as scales go, as long as they work at any fret in standard tuning, they'll work in Eb, because it is a standard tuning (just lower).