Do you know how many updates you got that day? If you can't find a way to remove them, can you restore back before the updates? Can you remove the updates?
I got several updates on the 28th, but I have an x64 system.
The Windows Explorer icon is normally pinned to the taskbar. I assume you still have that one. Maybe try unpinning it to see if anything changes. Does the link work?
On the Homegroup one, are you a member of a Homegroup. Maybe leaving the group would help.
Can you check its properties and see any information about it that might help?