How to create a content-type with "sub-pages" that are default and/or custom per node
Everything you've described is done by OG (Organic Groups).

OG is originally designed for GROUPS to have 'private' sections of a website, or to manage how groups manage different parts of a website, but the side effect of that allows you to build highly contextual "sub sections" of a website just like you're describing.   

All of the 'contextual' stuff you mention.   Site side branding, sub section branding,  site wide menus, section based menus.  Are covered by OG.

Good luck!