Privacy Implications of using ISP issued Router? - eviltoast

I know this is an outrageously bad idea, I don’t need convincing. I am just looking for some more information and discussion on what exactly the exposure and surveillance risk is.

I’m asking both for my own education (I am still very green to networking), and to better explain to people in my life if and why they should care.

  1. Is it true that traffic can be tracked and logged by ISP through DNS lookups, as these routers are preconfigured to use their internal dns service?

  2. If this is changed (like base.dns.mullvad.net), how much does this actually mitigate the risk here?

  3. What about when a VPN (mullvad) is also being used at all times? Would it then be “overly paranoid” to fear this untrusted box all the traffic goes through?

I personally take a conservative approach to things like this and assume it’s an unacceptable risk, but I don’t really understand what the truth is.

Thank you in advance for your time and thoughts.

EDIT: I’m asking about US and US adjacent areas