1. Yes, it will work with Office365 (hosted Exchange server) - everything in the pst can be moved to the exchange mailbox and will be available using web access or outlook. Outlook.com/Hotmail only supports Calendar and contact sync (and email of course).
2. Outlook 2007 is fine. The only differences would be features available (like the ribbon etc) - data would be the same in all 3. One suggestion - if you use the Journal, stick with 2007 as long as possible as its broken in 2010 and mostly gone in 2013. (The journal folder is in 2013, but the automated journal features are gone.) If you decide to upgrade, buying outlook 2010 now qualifies you for a 1 yr free subscription to 2013.