1) Yes, you have to compile it yourself using your newer perl.

2) mod_perl will search the @INC that it reports for installed modules. If your question meant something else, please elaborate.

3) You can't - the mod_perl package depends on the perl package.

If you want to use a newer perl for some reason then you would be better off compiling and installing it and its modules (including mod_perl) yourself and ignoring the system perl entirely. There have been many, many discussions about this here in the past.

As an aside, Rocky 9 will be out soon since RHEL 9 is in late beta so if you just want something newer than 5.26.3 then maybe wait a few months and you could use that as your distro and have it all packaged for you.

Does it matter under which user I install perl-modules using cpan? So far I use root because I get some permission issues e.g. while installing DBI.

It matters. You must install as root if you want to install them in a directory which is only writable by root of course. But maybe you don't need to install them there? Either way, only install as root - don't compile or test as root for security reasons. cpanm has the handy --sudo option for operating in this way.