BuddyPress.org

@optimized You will need to code for it, it can be done with custom coding.
You can use user_meta to store parent member info or organization info which can be populated at the time of registration.

@optimized Private messaging is available at the individual level, you can use https://wordpress.org/plugins/mass-messaging-in-buddypress/ to send a message to all group members or extend the same

@optimized You can check https://wordpress.org/plugins/buddydrive/

@optimized You can create the group from frontend only.
You can also limit the group create feature for admin only from BuddyPress Setting

Setting >> BuddyPress >> Options

@optimized You can try https://github.com/wbcomdesigns/bp-redirect