They are currently different sections. New is all user submitted in real time. Hot is those images that have already proven themselves on the web. Hot sorted by time is the old new. 

Please email support@imgur.com. 

You're welcome!

The old new is now hottest sorted by time. The new new are images being added in real time. 

This is already a feature on the new site from your gallery profile.

It's on Facebook's end. You can email support@imgur to get access to your account. 

Imgur uses the JavaScript function called PopState in order to update the URL of the image. IE is a bit outdated and doesn't support this. IE 10 is rumoured to, however. You should switch to Chrome though :)

This is an error on Facebook's side. Please email support@imgur.com to have your account dissociated from FB.