Hi Angela. For your issue about synchronizing your Hotmail with Outlook, please visit this link.
Visit:
http://windowslivehelp.com/solutions/settings/archive/2009/02/16/how-to-add-your-e-mail-account-to-microsoft-outlook.aspx
And about synchronizing your calendar to your phone, please contact Microsoft Mobile Support about this.
Visit:
https://support.live.com/eform.aspx?productKey=wlmobile&ct=eformts
I'm sorry; I tried but I'm unable to recover your missing messages.