From my perspective there are two issues with your plan – Git and “conventional” structure. So basically everything. 🙂
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Git (and version control in general) is a poor tool for whole site stacks. Been there, done that, it hurt a lot.
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What you call an “unconventional” structure with content separated from core has been a very conventional and robust choice for any serious site for a while.
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There are pretty much no turn-key ways to combine whole site stack with native updates. It just doesn’t go well together since it tries to achieve different goals in projects of different levels (developer in control vs end user in control).
If you ask me the best bet for whole site WordPress stack is currently Composer, however opinions may wary. 🙂
On your specific concerns:
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As above – native updates (more so auto) don’t play well with tightly controlled stacks.
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WordPress core isn’t developed in Git and doesn’t accept pull requests, all contributions are (so far) via patch files to Subversion.
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You’ll likely have to commit such plugins into your repo. Or go with another approach like Composer.