Is there any way to post new questions on an IRC channel?

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Not out of the box, but it can be configured to do that.

The repository version (not released at the moment) has the "new_question_posted" signal, which can be connected to the IRC channel or something else.

You can create a bot that reads the RSS feed from the site and post to IRC when it gets a new element or you can connect it with the signal as @Evgeny's answer.

There are a few irc bots projects written in python like bosnobot or pythonircbot that you can use for this.