Depends on your security model IMHO. If unencrypted dns traffic on your network, or your router being a possible aggretion point for dns requests from devices on your network is fine, then it is a great way to simplify using it for your network.
No, but your OS needs to be configured to use the DNS server on your router. Easiest way to do this is with DHCP + NAT rule to ensure all DNS queries are processed by your router.
It's not necessary but it ensures that all DNS queries are processed by your router. It could be that there's software that uses a specific DNS server hardcoded to make sure they can avoid your Pi-hole (or alternative solution) to track you.