Exchange not updating busy
Federated sharing features require that the Client Access servers in your organization have outbound access to the Internet by using HTTPS.
You must allow outbound HTTPS access (port 443 for TCP) to all Exchange 2013 Mailbox servers in the organization.
In organizations that contain both Exchange 2010 and Exchange 2013 servers, users who have a mailbox on an Exchange 2010 Mailbox server can use organization relationships to share free/busy information with recipients in external Exchange 2013 federated domain organizations.
The Exchange 2010 Client Access and Mailbox servers must be running SP2 or higher, and you must have at least one Exchange 2013 Client Access server in the Exchange 2010 organization.
This is working correctly and I can see free busy 2 ways between the O365 tenant and Exchange 2010.
Additionally user have sent calendar sharing requests both ways and can successfully open calendars and view content in Outlook 2013.
You may need to coordinate schedules with people in different organizations or with friends and family members so that you can work together on projects or plan social events.
With Exchange 2013, administrators can set up different levels of calendar access to allow businesses to collaborate with other businesses and to let users share their schedules with others.
The only way I can find for them to see the newly added entry is close and re-open outlook - this seems to "refresh" the calendar.I worked my way through every setting I could think of, including (but not limited to) Autodiscover, DNS, permissions, certificate settings, Exchange CU level, to no avail!Also, if you haven’t seen this before, the hybrid environment free/busy troubleshooter was actually a great help in systematically working your way through potential problem spots.For Internet sharing policies, external users access either a restricted or public URL on the Client Access server.For details about how to configure free/busy sharing between common Exchange deployments, see Configuring federated sharing between Exchange organizations.