Software with phone-app and web interfaces to create impromptu groups and discuss

Question

We students have ten subjects taught by ten different teachers. We created a Google Group to share info, but it has two problems:
1. When we or any teacher posts to the Google Group, all teachers receive the email even if the info is not relevant to them (they can of course switch off email updates, but that's not the right way to solve this).
2. Some students still use non-Gmail ID's as their primary ID, and are reluctant to use the Google Group.

So another student created a WhatsApp group (because it does not require any login, and even the head of the department likes WhatsApp), but few students do not want to install WhatsApp because it needs to be installed on their phone, and they don't want to do that. They want a purely web interface.

I considered Facebook, but I doubt we'd want our teachers on our social network.

So is there a free software option that can:
1. Support multiple group creation without any hassles (kind of like the concept of "circles" in Google Hangouts"?)
2. Allow people without a GMail ID to easily be a part of the group.
3. Has a simple and quick way of access via web and phone-app? Preferably with options of alerts and email notifications too. Basically, students won't want to create a new login and password. They'd prefer to use their existing email ID (which is why Google Groups or Google Hangouts was great, but the guys having Yahoo and Hotmail ID's didn't like it).
4. Has options for chat, topic-based group discussions, image sharing and dropbox/Google-drive link sharing?

Answer 1

How about email itself? If you don't include a teacher in the recipients list, they won't get a message.

1. multiple group creation — Just create a group of contacts in your address book.
2. Allow people without a GMail ID to easily be part of the group — You can use any email address.
3. a simple and quick way of access via web and phone-app — You can use your favorite webmail interface or email client.
4. Has options for chat, topic-based group discussions, image sharing and dropbox/Google-drive link sharing — All of these are supported by email in a direct fashion, except for chat, if by "chat" you mean synchronous rather than asynchronous communication. If you need that, it's probably best to use some other service that doesn't require creating an account, like IRC or Discord. That said, people these days have gotten in the habit of using asynchronous media (like SMS) as if they were synchronous, anyway, so do you really need this? In fact, there exists a program Delta Chat that provides an instant messaging-like interface for email.