Anyone? Or are there plugins for some of these features?

- In groups, when a user posts something does/can it email all other users in the group, that something has been added. 

Answer:

- Can a user subscribe to other users so that when they add something they are alerted?

Answer: 

user can follow other members, the activity of those members will be displayed in the dashboard newsfeed. 

- Can we upload/attach documents (pdf, word, excel, etc) in order to share

Answer:

you can add these extensions to the allowed ones. 

- Display events, etc in a calendar view

Answer:

this is considered as a custom code modification, also you may search in the store, there might be a plugin developed to satisfy your needs.