Will this slow down the site or require more bandwidth.

Not at all.

Excellent = 5 stars

installed under test

So if someone with the username Bob enters the chat, will their name automatically be Bob in the room?

Is there no usergroup permission setting ?

yes as long as someone has not registered that nick in IRC.

Since IRC is accessible using any irc client (desktop, web, mobile etc), there is no benefit in blocking it by usergroup as anyone can join using those methods.
What type of usergroup permission are you looking for?

So what does it do if the user's name is already taken on that network? Does it change their name to that but then the IRC tells them to login etc?

edit: nvm, tested it. puts an underscore after name

If username is taken, it will ask for the password. The user will be renamed to Guestxxxxx after 60 seconds if password is not provided.
If username is taken and that user is online, username will be changed to username_.
This is standard IRC behavior.

Demo is working. If it doesn't load, it means the qwebirc is unavailable at that moment (usually due to updates).

can i create my own irc server?

You need to run an ircd in your server.
http://en.wikipedia.org/wiki/IRCd