1)They released the patch again which update your windows live mail to a newer version.
2)Is using your browser as a alternative in the mean time ,a solution or you need offline mails , other apps integration support? You can set all browsers these days as a icon linking direct to your inbox and store your password and set it up as 2-step authentication allowed program. Stuff is changing on a day-to-day basis that is hard to keep track of what they fix,broke,fixing,broke again :P.
3)Been trying to fix my neighbours Windows Live Mail 2012 and testing it on my own PC , I have noticed the strangest syncing issues from timing out to errors like you stated but literally 2 second later syncing again goes without a hitch. I made screenshot of my IMAP setup here which seams to work most of the time. http://answers.microsoft.com/en-us/windowslive/forum/livemail-sync/kb3093594-windows-live-mail-essentials-2012/af2e36b1-5c6b-432a-870d-62aa998e4269 , it seams as far as i can tell the same as yours except the IMAP-mappings and the port but that shouldn't matter , i think.
4)What is the folder called you can not sync and is it already shown in your inbox when you go to outlook.com.
It looks like our settings are similar.... I did change my SMTP to 587 to match yours.
4.) The folder is labeled 'work' and its updated on Outlook.com and the Windows Mail App. It just won't download or update, sync on WLM.