If you are switching to Microsoft Office365, then the 'Allowed to Send Outbound' list should have all of Microsoft's 365 IP address ranges. They can be found here:
https://technet.microsoft.com/library/dn163583(v=exchg.150).aspx For the Mail Routing, Microsoft will provide you with a FQDN to use, something like 'yourdomain-com.mail.protection.outlook.com'. This is the value that should be entered in the right hand box instead of a specific IP address.