פרסומים שנוצרו על-ידי Howard Miller

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I don't know and it would be interesting to know if it makes any difference.

What I wouldn't do is to point it at a relatively slow shared folder. As it's a cache it should work fine pointing it to (fast) local storage. I suspect that if it's pointing somewhere slow it'll make things worse. There's also (I read) a potential security issue, in that the cache will contain code that is executed. So presents a vector for hacking if it's not locked down enough.
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Firstly - and I mean this in the nicest way - you haven't understood how roles and capabilities work.

It's almost always wrong to say "I need this to work for teachers". You should code things to work for particular *capabilities*. For example, you may want to check if a user has the capability to edit a course. This then works now and for any other roles you might create in the future that have that capability.

Unfortunately, you have another problem. Roles are allocated in what Moodle calls contexts. More often than not courses. So, you can't customise the login page because Moodle doesn't know who you are. Worse, even when you've logged in everybody has the "authenticated user" role. You're not a teacher, student or whatever until you enter a course. Any given user could be both a teacher and a student in different courses.
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Using standard Moodle, there is no way to have dedicated admins. It's the whole site or nothing.

If you can live with creating users centrally then you can create Course Categories for each School and assign users with the Manager role to each course category.