Not sure if you could do this by polling repo with RSS reader with specific parameters. I don't know how but quick googling around that has been suggested previously.

And you can get "new" from AliExpress around 80-90€

I don't know but they do. I picked the cheapest name I could find and went with it.

Checked and they still do sell domains for 10y but price has gone up.

I bought domain from joker.com, 10 years for $33

I just use steamcmd (depending on the game) and make my own launchers for each server. It isn't ideal though so i might check that Pterodactyl myself, forgot that it's a thing :)