WRONG.

Your problem concerning the domain is barhemmungslos.de/ is that you have NOT correctly defined it in your HTTP administration tool.
You show yourself that you have assign the domain name barhemmungslos.de/ with the "root" directory and NOT with the deployed directory.
The reason is that you show that when you add the subdirectory "barhemmungslos.de/multisites/u62sHemmungslos/"

It this is working, this is because you have setup the "{root}" path and not the deploy directory that is {multisites}/u{user_id}s{site_id}

In addition, you have again create inconsistency between SITE and MULTISITES directory.
www.jms2win.com/download?page=shop.produ...35&category_id=1

You have demonstrated by your result that you have NOT put the EQUAL values between the domain definition and the deploy directory.

In the barhemmungslos.de/ you have assign {root} and in JMS you have assigned {multisites}/u{user_id}s{site_id}
They are NOT identical.

You don't have to modify the .htaccess to fix you HTTP server configuration that is currently wrong.

If you want that we setup your environment, we have a billable support that you can order at