The API handles most shit like logging in, Q&A and profiles. The chat server is seperate and handles... chats. If the API is up and chatting is down (You) can still drool over catfish even though you can't ask them if those tits fart.
>Why does it say we couldn't send an email there when the API is up?You probably got banned.
>What are those links supposed to look like when they're working?The API link should show a single line with the active user number, the chat link should show you an error about websockets. If you see anything else, it's down, regardless of what this website reports.