I know now why it did not work, 'cause in the middle of the night i just tried one thing, and now the site works.
It is like this now in the .shtml files:
<!--#set var="path_info" value="${PATH_INFO}"-->
<!--#include virtual="/cgi-bin/index.pl$path_info"-->
As you see, i had to use SSI-variable to pass that PATH_INFO to the CGI-script. There was no problem with Perl, but what i read at night, Apache will not for some reason pass PATH_INFO and QUERY STRING with GET-method to SSI-included file, but you can get away like this.
I figured this out with luck, phuuh!