I used the template editor and tried to make some changes to a copy of the default citronate template but trying to safe it I get the error message: "You don't have permission to access /index.php/admin/templates/sa/templatesavechanges on this server."
Any idea how to solve this?

Check your directory permissions - www.limesurvey.org/manual/Installation#S...irectory_permissions

Thank you for the hint. Unfortunately didn´t work.
I changed the owner for tmp, upload and application/config to www-data and set permission to 777, too.
Result:
Forbidden
You don't have permission to access /index.php/admin/templates/sa/templatesavechanges on this server.
Apache Server at survey.tenckhoff.eu Port 443

If 777 is correct depends on the settings of Apache and PHP. Some setups will prevent 777 at all. You really should contact your provider Strato. Not sure what package you're using. You should read the logfiles of apache and php (depends on your setup) if you have access to them.

Thanks, Strato won´t help because it is my own server managed by myself. Checked the protocolls but did not find something usefull to solve this issue.

Try 755 on /tmp, /upload and all sub-directories of /upload.

It's a bit of a downgrade to be only writable from the owner but weirder things have happened - some of my clients' hosted accounts are 777, some are 755.

What exact Strato product are you using and which OS image is installed?
What webserver is used and which PHP handler is configured?
Some common php handler are:
suPHP (Single user PHP)
DSO (Dynamic Shared Object)
FCGI (FastCGI)
CGI (Common Gateway Interface)

It´s a root server, OS= ubuntu LTS 14.04.3 (all latest updates installed), php is configured as FCGI.