Calendar: AquaMail syncs your Calendar with "the system" and you can use any Calendar app (built-in, Google Calendar, etc.) or widget.
Contacts: sorry at this time Exchange contacts are only available on the app's compose screen:
- In the recipient entry fields (auto-complete)
- In the app's own contact picker (the icons to the left of each recipient entry field).
"Proper" Contact sync is planned, but not there now and I'm not yet working on it (current "big" feature is push mail for Exchange).