You should never expose a DNS server publicly. Connect to your VPS through a VPN like Wireguard.
Do you have a second DNS server configured in Windows which it could use as a fallback?
There is https://gitlab.com/flauncher/flauncher, which is working nicely
Yes, https://containrrr.dev/watchtower/ is a great tool. Used it myself for a whole now.
https://www.wireguardconfig.com/