This sounds like an exciting project!

There are certainly a lot of points to consider when putting together anything involving memberships, especially something like you've described. However, I won't go into every possible course as I believe the most likely route that will bring you success will be leveraging WordPress' multisite capabilities.

Essentially, I'd be recommending you setup a multisite where schools can sign up for their own subsite on your network. It is possible to pre-configure your new sites so that upon signup, each school gets a site with the theme, plugins, content, settings, etc. which you wish them to have. You can assign each new user with specific roles on their own site and your main site so that they will be able to participate in things like site specific or network wide forums.

To facilitate this, I'd envision using several plugins including:
http://premium.wpmudev.org/project/pro-sites/
http://premium.wpmudev.org/project/new-blog-template/
https://wordpress.org/plugins/buddypress/
https://wordpress.org/plugins/bbpress/
https://wordpress.org/plugins/join-my-multisite/

There are a number of reasons why I'd recommend this approach but I'll just mention a few important ones:
- This approach would allow you to bill the organization rather than the individual user (if desired).
- Allows for the simplest management of groups of users for active/inactive accounts.
- Organizations can have their own environment, complete with private groups, forums, content, media, etc.

Those are just a few reasons why I think this approach would be effective and appropriate. That said, I would say with certainty that a site like you've described could be built on single install of WP, simply taking full advantage of plugins like BuddyPress, bbPress, the many complimentary plugins for those and/or potentially some of the many other powerful membership plugins for WordPress.

I hope this is helpful. Please indicate if you'd like more details on any specific point. I'm happy to help.

This is certainly possible in most cases. As long as these two points are true, you're in business:

1. You have permission to repurpose the content from the original source.
2. The source has an RSS/Atom feed.

If those are both true, than you can do this one of two ways:

1. Use a plugin that exists. There are numerous plugins out there which can create posts from a feed. Some are very simple and others are quite complex. It doesn't sound like a simple one will work well for you though as you have criteria you'd like the entries to meet.

Something like this one: https://wordpress.org/plugins/wp-o-matic/
Or this: https://wordpress.org/plugins/wpematico/
Or this: https://wordpress.org/plugins/wp-rss-multi-importer/

By no means is this a comprehensive list or an endorsement of those plugins. It is only to show you that a quick Google search can turn up loads of plugins loosely matching your criteria.

2. You could have someone develop a custom plugin for this. Your request is not very complicated but there are subtle issues with it such as the fact that you probably want the entries to all be created in a Draft or Pending state, you may want to use multiple sources and you will only want certain types of entries from those sources. I would expect there to be existing plugins which do this already but there is a chance that you'd be better off getting a good developer to put something like this together for you, just to make sure it works exactly the way you want it to. There are many great WordPress developers out there who would consider this a relatively simple project.

I hope this helps.