It's probably not a static-ip and I wouldn't rely on it as such. I'd use http://www.duckdns.org/ to handle the dynamic IP issue (or something else, https://freedns.afraid.org/ would be another option)
I'd look to pihole to start with for DNS. It blocks ads and you can add manual DNS entries. If you need something more complex, you can always migrate to something like unbound but pihole is a good, easy start.
Setup https://letsencrypt.org/ You didn't mention HTTPS/SSL, but you should really set it up. let's encrypt makes it easy and free
Not all I self-host but pihole, plex, & homeassistant are certainly my most used.