The more interesting part is, whats inside the folders? Especially the .htaccess files might be interesting. I mean the content of it, because if theres a mistake there it might end up in a 5xx or 4xx error page.
Plus, the content of the problematic vhost files.
Display MoreFor the (www.)19.bundesschülertagung.de I get a Dollibar Login screen
for (www.)bundesschülertagung.de I get an i-MSCP 403 forbidden
and for http://www.bundesschülertagung.de/index.html or index.php it says Page not found.
Try to locate my access (11:37:40 MESZ) and find out where apache tries to locate the documentRoot....
Since I also get an 403 when calling http://dmn20.configpanel.<yourdomain> I think you have to have a closer look into the documentRoot...
/J
I'm sorry, but the access-log doesn't got it - it seems like stopped on Mar 30, since then there are no access logs....
The more interesting part is, whats inside the folders? Especially the .htaccess files might be interesting. I mean the content of it, because if theres a mistake there it might end up in a 5xx or 4xx error page.
Plus, the content of the problematic vhost files.
Files in attachment -- there are no htaccess-files …
At the moment, at least for me, its unclear whats the exact issue. I kind of lost the overview here. Sorry. 
Because there are now like 10 domains with different information and some key-information arent provided at all.
It might be usefull if you do the following (be as specific as possible):
Which domain got a problem?
What kind of problem?
Screenshot of the configuration from the domain.
The content of the vhost files for the problematic domains.
Plus provide information which seem be be important for you, but please they need to be specific and the more detailed the better.
Which domain got a problem?
It's bg.de
What kind of problem?
When I try to get any data from that domain (e.g. the index.html oder index.php files, the server only gives an error 404.
Screenshot of the configuration from the domain.
The content of the vhost files for the problematic domains.
default server 19.xn---u6b.de (/etc/apache2/sites-enabled/19.xn--bundesschlertagung-u6b.de_ssl.conf:1)
port 443 namevhost 19.xn---u6b.de (/etc/apache2/sites-enabled/19.xn--bundesschlertagung-u6b.de_ssl.conf:1)
alias http://www.19.xn--u6b.de
alias sub20.configpane.de
port 80 namevhost xn---u6b.de (/etc/apache2/sites-enabled/xn---u6b.de.conf:1)
alias http://www.xn--
alias dmn20.configpanel.my-domain.de
Plus provide information which seem be be important for you, but please they need to be specific and the more detailed the better.
At the moment I don't have any more information.
http://www.bundesschülertagung.de/index-3.php
your screenshot shows exactly one file - the index3.php
This shows a 503 error (in contrary to the 404 with other file names - or the 403 without file name).
So - the file is found but the php inside throws a 503 error...
What are the problems now:
- logging in apache? -> we have to have a closer look at the corresponding include-file
/etc/apache2/sites-enabled/xn--bundesschlertagung-u6b.de.conf
normally you should have a log folder for each site...
/var/log/apache2/xn--bundesschlertagung-u6b.de/access.log
If Logging does not work for all sites/domains, then something with the vLogger-Script seems to be wrong
/usr/local/sbin/vlogger
/J
That what you posted as the vhost file, isnt actually the vhost file.
Do you use any plugins for i-MSCP?
Is the i-MSCP version up to date?
Is there a .htaccess file in that directory? Keep in mind, that you need to search especially for hidden files.
Try to delete the file and upload a new index.php or index.html. Use the following content:
Did you change something manually?Is that a new installation?
Try "/var/www/imscp/engine/setup/imscp-reconfigure -r httpd" . If that doesnt solve it, you might try "/var/www/imscp/engine/setup/imscp-reconfigure -r all".
If you do that commands, make sure to disable any used plugins before you do it (better safe than sorry).
What joximu posted is actually a very good idea. Why didnt I thought about checking the access and error logs from that domain? 
Whats inside the htdocs folder?
How does the vhost look like?