This depends on the platform. But for most platforms, you can use your favorite IPTV server (Jellyfin and NextPVR are 2 popular ones) and connect your TV to it. Then you can watch and record it on your TV!
Direct: http://tommyweather.loseyourip.com/TWLive
Playlist: https://techytommy3.github.io/weather/TommyWeatherStream.m3u.
I probably know this. Wait a few minutes. If it doesn't come back online, email the Tommy Weather Emergency Mailbox.
(Simple version) All information comes from the National Weather Service.
(Advanced version) The data gets transmitted over XMPP on the NOAA Weather Wire network. Additional information comes from api.weather.gov.
Yes! Please do!