You can run as many instances as you like.
Key deactivation means the key is permanently blocked, and this only happens if Badspot does it manually, which basically requires a key to continuously bounce all over the world faster than anyone could travel, as if it was compromised and shared online.
Authentication fails happen if the key is running simultaneously on multiple IP addresses, or if the name is changed while playing. And all that happens then is you're kicked from the server with the message "<name> authentication failed <IP>" and you can rejoin (provided the host wasn't paranoid and thought the message meant you were hacking and banned you, I've seen that happen)