I have thought about this more than is healthy for a middle aged adult male.
The flavor should be similar to the third edition of the game, which I have fond memories of (despite being somewhat unplayable). A weird, unrealistic post-apocalyptic mashup...but not silly. Basically, if you can imagine it in a post-apocalyptic sci-fi story, it has a place in Gamma World.
Yes
Yes, although mechanics should be provided for GMs to make GW their own.The mechanics should be very similar to Rob Schwalb's Punkapocalyptic, if it used 5E as the base. Ten levels. Race should carry more mechanical weight than core 5E. Humans, mutants, mutant animals, mutant plants, robots, and extraterrestrials/extradimensionals. Three to five classes. Then gobs of subclasses that can be taken by any class, which is how you get lots of customization relative to page count. Again, Punkapocalyptic has a great take on this.
Feats which are basically dips into class/subclass features. They can have level requirements but no other prerequisites.
Obviously gear should be important, so a long list of gear ranging from stone age to medieval to modern day to futuristic. Some of which you can purchase, most of which you can't.
Same as above, mechanics should be provided for GMs to make equipment on their own.
An 100 page bestiary. Cryptic alliances, factions, tribes.
Cf.
A map of the United States and then a close up of a single region with a sandbox campaign that's 30-50 pages long.
I am of course most familiar with the US; but I could see doing two sandboxes - one US, and another wherever D&D is most popular outside the US.
On board with this 1000%.Publish it all in one volume. Open it up on DMsguild. Launch it with an Adepts program so that there's some interesting expansions available as PDFs from Day 1. Then leave it alone for the next 20 years.