Go to settings>users and create a new user with admin priviledges. Make sure that user does NOT have an email address. Just a local user (so keep clicking the text that says "save user without email address" and so on.
Log out of your account and log in as that new user. Your PC will now finish updating the new user and part of that process involves downloading the patches you can't get in your regular account.
When first logged in, go to the windows store, and you should automatically download updates after 10 seconds.
Once updated, restart the PC and log into your regular account. Mail and Calendar should work properly. Go into Windows Store. You should be able to download the rest of your updates now.
Keep that account you made as an "emergency backup"; don't use it for anything other than this type of trouble. As a Windows Insider, I was stuck the same way back on build 10071 and did the same thing to force Win Update to get me to the next build.