Very first message states:

MYSQL server has gone away...

Your host has a problem with MYSQL service they are offering you.

They must address this and fix it.

susommer wrote: the hoster says there's nothing wrong...
Is it possible that something went wrong during installation that could cause this?

Can I try to install again, over the previous installation (like a manual update)?
Would this work at all AND would all the settings and plans and whatnot still be intact?

Thanks,
Susanne

If MySQL *goes away*, there *is* something wrong. If your hoster says that nothing is wrong, then maybe it's your hoster...

You can do an install over of CB and CBSubs, that's not an issue and will keep your settings. Backup first as usual, as your host is not reliable, and results can this not be deterministic....

The issue is that your MySQL SERVER is not reliable, also visible in those warnings. Nothing to do with our numbering.

Nothing to do with our scripts but an issue with your server (and your *hoster* if he says it's not his server).

If the hoster does not understand error "Mysql server has gone away", then do not loose more money with him and change hoster.

We are not going to accept money or spend free time, as we are not able to help you for issues that only your hoster can fix (or more precisely only you by changing hoster to a more professional one).

There are many reputable Joomla hosters (hint: do not look for budget hosting): Rochen, Cloudaccess and we do offer secured high-availability business hosting too ("Hosting" menu at top).