Yes. Just set your secondary dns in your client to whatever dns you were using before. It will fall back on secondary if primary dns via pihole fails.
Sometimes the secondary will take precedence over the primary even though pi-hole is reachable.
In my experience, Windows is the worst offender for this. *Nix, macOS and iOS will always prefer the first resolver if all other variables (ping, availability, etc) are equal.
I can't remember the details but something changed in Ubuntu defaults to make default to distribute the DNS calls rather than order nameservers, it can be set to use order preference.
In short, don't assume strict ordering on Ubu, at least.
Install a second Pi as PiHole as well. It also runs fine next to Kodi or so if you have one already. DNS requests are incredibly small.
Sure. I put in your second DNS as .. seconds DNS.
My routers DHCPD gives pi-hole as primary and itself as secondary DNS.
It seems that both primary and secondary are being used in round-robin and the primary gets relegated when secondary happens to answer faster.