Syncing options...

Natively, Windows Mobile was only intended to be synced with Outlook, so Windows Live Mail and the like is insufficient. There are third-party applications that can sync to/from other email/calendar applications, but with Windows Mobile being dropped by Microsoft, there's little development on that front. Specifically, SyncExpress was the best option with Windows Vista's built-in mail/calendar applications, but it was never updated to support Windows Live applications once Windows 7 dropped the native applications. You can still do it manually with something like PIM Backup, but that's far less than ideal.

Perhaps someone else knows of an alternative, but I am afraid your options are limited.