I have a contact who hasn't been online for over a month, yet in the what's new tab at the bottom of the window it says they have a new display picture which hasn't shown for me. I am starting to wonder if I have been blocked - would this still be displayed in the what's new tab if this is the case?

No, if you block someone you don't see information in their "What's New" tab.  It might just be that they've only ever signed in while you've been offline.  You wouldn't see the new display picture in Messenger (as they only change when BOTH contacts are online), but it will get added to the news feed in "What's New"

Also, what about personal messages? I've noticed there have been a lot of them posted on the what's new tab, but I have still not seen them online at all.

The same thing applies