Wow, great ideas! I really appreciate the attention to detail with things like the color being computed from the name to ensure cross-device consistency!
Generally I love the direction! I have one key concern:
I'd like to see some mockups of what this would look like the first time you open the app (the zero case). You've described the one and many cases nicely but I'm not sure what happens when there are no profiles. What is the icon going to be? How will users know what it means if they weren't the ones to choose it? If it's D for Demo, how do they know what it's for?
I appreciate the desire to keep the UI clean and re-purpose the menu icon space with the profile icon, but now the affordance of the well-known menu icon is gone. I think it might be worth exploring having the profile icon, name, and URL shown above the 'iconic buttons' on the home screen. It would look nice, and it would make a lot of sense. "Turtle nesting: Fill blank form, Edit saved form ... ".
The menu could stay as it is with the options being 'General Settings, Admin Settings, Profile Settings, [divider], Change Profile, Add Profile'.
This also has the added benefit of getting rid of these buttons:
Which seem kind of awkward to me.
Thoughts?