What does "psql: /usr/pgsql-11/lib/libpq.so.5: no version information available (required by psql)" actually mean?
You have installed a mixture of packets: some from the Fedora distribution, some from the PostgreSQL Global Development group.
These don't work well together. In particular, you have psql from the Fedora packages in the PATH, but libpq from the PGDG packages is on the library path.
That explains your question #2.
Ad question #1: that warning is printed if the library version of the installed library is lower than the one the software was linked with.
Remove the Fedora packages to get rid of the problem:
dnf remove postgresql postgresql-server

I hope that puts the correct psql on your PATH; if not, reinstall the postgresql11 package.