I am sure if you use DoT or DoH it's going to be very hard for ISP to block using your own DNS even if you rented a modem/router from them. It does need client-side support though.
For extra points you could deploy a firewall which intercepts all DNS requests and forwards them to that machine. Some apps have hardcoded DNS servers and ignore what you have configured.
Not really! You can buy a router that ships with OpenWrt out-of-the-box and just toggle a little checkbox. Plug that into your ISP's router (or use a wireless bridge in client mode, that's supported, too) and connect all of your devices through that. Now all your devices use DoH and don't even know it.