I have a rpi set up with a minutely cron job to update my domain name to point to home. Works pretty well. At the worst you lose connection for a minute but usually the IP address only changes when the home connection fails which can take more than a minute to reset anyway.

Dynamic in theory, but for many people the IP is unchanged for a long time. I remember reading an article that said the average length of time between dynamic IP changes tracked by some company was something like seven months, though I can't find it now.

I have cable with a theoretically dynamic DNS but it's changed once in >4 years.