You may already have experienced this kind of situation from the other side of the screen. For someone who is not used to the chat, you may think at first sight that you are dealing with an automatic tool, a robot that answers to your questions. Some internet users may be a bit direct in their way of speaking to you, before they notice that they are really talking to a human person.
They may forget to say you hello for example or they will ask a question without politeness.
As a matter of fact, it is pretty funny and rewarding to observe the change of tone when he realizes that he is talking to a real person !
In general, try to be honest and transparent ! Don't hesitate to say that you don't know the answer or that you don't agree with the visitor. You are an expert, not a professional agent. Even if you do have to respect the brand and the website, you are not there for advertisement in disguise.
The other internet users like to talk to you because you are authentic and independent. They are lucky to have you :)
Rude Internet users
You may have to deal with disrespectful people. But it should be an exception. Please don't take it personally. It must have been an angry person who's only goal is to bother you. In this case, keep calm, take distance and make it fly by. You are not there to get into trouble !
You can start by telling the person that she should calm down and explain her that you are also an Internet user like her and that you are here to be helpful.
Example : "I'm a member of the community. I'm here to help and to share my knowledge. Please remain polite and respectful !".
If this person doesn't want to calm down, stop the conversation, warn the community manager or block the visitor by yourself so that he can't use the chat anymore.
Don't hesitate to share this experience with the other members of the community in the livefeed. They may have experienced such a situation and could give you some hints to cope with this kind of situations.