Azure AD close collaboration between two organizations

For the calendar requirement, you can configure Org Relationship in both ends (in ECP)
But for other requirements you can try below.
* Once the Guest account is created, use MSOL PowerShell module to change the user type from Guest to Member. The user's UPN will still be that long string, but they will act as normal members in Azure AD.
With this conversation, you can try adding them to SPO sites for permissions etc.
Once the Guest is converted as a member, you can use Azure AD PowerShell module to allow them in the Global Address List.
https://docs.microsoft.com/en-us/azure/active-directory/external-identities/user-properties 
If that user object has "Directory Reader" role assigned, I noticed that Guest will be able to see the users in the Guest Tenant (Teams, SharePoint etc.)

However I also noticed "Cross-Tenant People Search" feature is in development in the M365 Roadmap and you can use this feature if both of the tenants are under the same business.

Hope this helps.