Using classic Outlook for Windows in business environments
Thanks for the screenshots. There are definitely problems syncing some messages. One option is to find and delete the messages that are listed - if its just those few messages, it should solve the sync issues. Hold Shift when you delete them so the problem doesn't move to the Trash folder.
But if you have a lot of messages that won't sync... did you try to import messages to sync up to the brightspeed server? Importing can cause sync issues. If you did try to import from a pst file, close outlook, go to %localappdata%\microsoft\outlook and rename the ost file (add old to the file name) then restart Outlook and give it some time to sync.