How is the infrastructure and bandwidth paid for?
For bandwidth intensive usage such as video, it will probably be "paid relays" instead of free ones. Click on url in the "Popular paid relays" paragraph to see examples:
Nostr is popular with the cryptocurrency community so the payment mechanics seem to favor Bitcoin and/or Bitcoin Lightning.
The media is hosted on regular web servers and it says you can host it anywhere. It seems like most of the videos are hosted here: https://nostr.build/
Which is a paid service backed by AWS S3