This did it for me :
Sign out of your account in the store.
Sing in again.
Go in your account details on the store and re-enter you credit card information, validate.
(I also changed my Phone number ... but I do not think there is an incidance).
Et Voilà I was able to update all apps without any error message afterward.
Hooray. No response from Apple to my open support ticket and/or to the threads here in the discussion forums, but at least for me the problem resolved itself last night and continues to function fine. I had confirmed it working on my devices last night and confirmed iTunes operation this morning. It appears to have been iFixed.
Interestingly, even though this problem was clearly fixed a few days ago, I've just received another email from the support person who originally replied to my message to Apple Support:
It's only me, XXXXX, from iTunes. I hope my email finds you well. I just wanted to send you a quick note to let you know that I haven't forgotten about you. Our engineers here at Apple are still working on a resolution to the error 11111 you encountered. As soon as I have additional information, I'll pass it along!
Many thanks for your continued patience and support - it's very much appreciated!
iTunes Store Customer Support"
So maybe someone is still facing that problem, but luckily all updates work for me now.