When it says "active now" on Facebook chat and then it says "active 1 minute ago" does it mean they were messaging someone through chat?
Not necessarily, just that a minute ago they had an application handling chat messages in the foreground (i.e. as the active window on their screen) - could have been the web application, could have been the mobile one.
According to various sources, it is when a message has been sent to that person. As a result, it's quite unreliable and doesn't mean they're “active” at all.
It's a nice way to boot you off his or her friends list (without actually doing it) by turning off the chat option on you. Since you haven't done the same thing to that person, that person will still appear as being online with a 1 minute timestamp. If you happen to turn off chat on that person then you won't see that person as being online anymore.
To the best of my knowledge, it indicates that the person has turned off Chat on you.