Each time your program loads, I’d request it, save it. If data exists and you got fresh data, overwrite it. If you get a blank request, API might be broken. So keep old data until you can retrieve fresh data.
Leave it to the user to select the one nearest them. Trying to use anything like GeoIP is never reliable.
Leave the value for “name” available to them in a drop down or radio list. Based on the selection set the URL template.
(Give them a field for manually setting the streamkey of course)
As for live.twitch.tv
I tested with OBS and tried to stream to it, connect was made, session ran, but for some reason my stream never went live. I assume there is some sort of de-sync or linking issue behind the scenes. I’m sure it’s being looked into.