Hi
It's always good to keep extensions up to date, but I always make a backup before updating in case something goes wrong.
I do not see anything wrong in ftp, but looks like problem appears not on every page even if not logged in. I cannot get into Your joomla panel since I do not know url to it. Regular /administrator is redirecting to frontpage.
Errors in console tell me that it's a conflict, so steps I would do in this case is to reduce the number of javascripts.
- first I would turn GK Tabs and NSP to jQuery library to get rid of mootools
- secondly I would disable module after modull till cart starts work, las unpublished before that happened will be the one to blame for conflict