I would like to have an account outside family sharing - can I have two accounts?

Yes you can but you can only be logged into a single account at one time, and transferring between accounts is not easy, particularly since you basically need both to be logged into the same Family Sharing group to do so. That kind of negates the whole purpose. :-)

This document explains how to create a new Apple ID (create an Apple Account) --> How to create a new Apple ID - Apple Support