You will have to fix this:
"PHP Fatal error: Uncaught ddl_change_structure_exception: DDL sql uitvoeringsfout (MySQL server has gone away"
or there is no further discussion/cussion about it.
"SQLtuner didn't work for me. Not enough privileges on the VPS-server"
Well, you are the only customer on your VPS, right?
Why couldn't you know/be able to use superuser credentials with your own
database server? In an ssh session to server you can su to root ... or even use sudo -s right?
Depending upon where you are hosted (provider name please), the operating system, somewhere on your system those superuser credentials are known and do exist other wise your site would not be able to be up when/if server is rebooted ... like after kernel updates. And I do hope your server is getting operating system updates.
I'll answer the above for you:
You are hosted with Linode.
Hints clues for superuser creds
https://www.linode.com/community/questions/1140/mysql-root-password
"You cound have a password set in /etc/my.cnf or ~/.my.cnf"
ssh into server.
where ever you land, see if there is a hidden .my.cnf file
ls -l .my.cnf
That 'dot' in front is important ... hides files from normal commands listing/viewing files.
IF it does exist, can you edit?
ls -l should have shown ownerships/permissions.
** don't do this one first ** repeat .... don't ...
https://www.linode.com/community/questions/17930/retrieve-mysql-and-root-password
Suggest that just maybe your best source for resolution to this lies with Linode helpdesk or even their community forums.
'SoS', Ken