Thank you guys for all your help and the replies.
1. @JayantaPoddar the Add Field produced the same error.
2. @BranislavBlagojevic & @Robert_LeClair by following your guide I was able to completely uninstall the 2.8 version, clean install it, renaming ESRI folder and all that you guys were so kind to suggest. However, the application continued to misbehave.
In addition, my tests included the creation of a new windows user that was able to replicate the error.
So...I once again completely striped down everything like your guide suggested, installed 2.7 with its 273_177550 patch and everything is working again as it should (leaving me with the stupid notification about a borked update).
So I guess I will skip this version completely and have my fingers crossed for 2.9, or maybe I wont be able to upgrade any more to a future version (without a windows reinstallation), which is a shame...