Create a private channel with customized UI?

Hi guys,
I am embeding RocketChat in my personal webapp, to use for chat communication. I have used chat widget for a one side communication using Live Chat. But I am stuck at the point that i need to create private channels for users to communicate with each other.

Can I automatically create a users account on RocketChat when user signs up in my personal webapp? If yes, can we create from live chat
a private channel for user to communicate with another user using our UI pop-up window?

Thanks in advance.