Well, I am actually just discussing a bug that allows that to happen with Brian in this topic, so you could try and use the same glitch for yourself.  Basically what happens is when a request comes in, it will display it on all operators screens, and then when it is accepted, it forgets to remove it from everyones screen. So technically you could accept the chat after someone else accepts it and just read what it written. Or you could view the logs after the chat as well

Spenser

Yes, I think it is 30 seconds per priority. So if an admin is on, they have 30 seconds to respond before it is listed in priority 1 screens, who have 30 seconds before priority two screens, etc