I tried then to print @INC in order to find out the paths to be checked for permissions:

So what were the permissions? ls -loanh ...

a) How can I (and most likely many other PERL programmers) fix that as normal users when lib.pm is "locked" by root's home?

You cannot fix permission issues without root

b) How can I install PERL in such a way that all users have access to the libraries and modules?

How did you install, did you save your install log?