I'm having friends come up in the chat bar that have no green dot next to their name. I'm just wanting to know if they are online or not? Some have green dots and some don't. Is it possible that the person is online but has clicked on appear offline? Any help would be much appreciated.
No, it isn't possible to know if someone if online and has just set their status as offline. It may arise a privacy concern.
But there's a way to know if someone is online or not by checking their profile, check if they recently liked status, page or anything which can indicate that they are active. But it won't always work.
There's another trick which can tell you if an user is active or not. Setup a group chat on Facebook by sending a message to more than one friend (also add the friends you want to know active status of) and then send a random message, now when someone in the group chat will see the message, there will be a notification like
Seen by [name] and if your friends see the message, the notification will be shown for them too.