If you want to use Grav CMS on shared hosting provided by 1&1 then make sure that you did all work it's needed to properly setting things up.

Logs

Change the logs destination folder to something else than standard /logs.

Here is available instruction how to do that: https://learn.getgrav.org/cookbook/general-recipes#override-the-default-logs-folder-location

If you use Grav CMS Problems Plugin you will have to comment out the line which is responsible for checking permissions for /logs folder. Unfortunately paths are hardcoded, so the plugin does not see that Grav CMS will use something else that standard path.

You need to comment out this line: https://github.com/bkostrowiecki/devnote/commit/2b7602def00ae20b80789e49bd7bd7a94b081e5f#diff-ee988a68fa86e0765c76277de23aa1de

500 internal server error on urls other that root

When your provider is 1and1 you need to have

RewriteBase /

In yout .htaccess. Otherwise any other URL than domain root will give you an internal server error.

Here is the guide: https://learn.getgrav.org/troubleshooting/internal-server-error#rewritebase-problems