Is using the router and modem my cable company provided for my internet putting my privacy at risk? And if so, I have heard of openWRT routers but it seems like there’s quite a bit of a learning curve with that but even if I got one would I need a non cable company branded modem as well? Any specifically that anyone here would recommend?
When you talk about network setup and IP addresses you have to differentiate between your local network (between your end devices and router) and the “outside”. Your devices connect to the internet through the router.
The IP gateway setting is your end device setting of which gateway to send packets through. You set it to your router. Whether this is done automatically (via “DHCP”) or not doesn’t make a difference in the end.
The netmask defines the network address space size. It’s also something you don’t need to change to set/change a DNS.
Where did you try to change the DNS setting? On your end devices would be enough. On your router it should also be a simple setting independent of other and of IP settings. (If the router allows configuration of it.)
(Did you set a static IP on your router, facing your local network, or the internet (would have to be provided by the ISP), or your end device within the local network (this is not necessary for DNS)? Either way I don’t see why it would be necessary to set a static IP address anywhere.)