Oh, I can definitely still use some help. I have a question:
Can I access a private irc channel in Pidgin that's hosted on Mibbit?
Mibbit is a web-based IRC client, just as Pidgin is a non-web-based IRC client (among other things). I don't think the Mibbit folks host any IRC servers themselves, but I could be wrong. In any case, user rights on IRC servers - like whether you can create a private channel or not - are handled entirely on the server end. In other words, if the IRC server allows private channels you should be able to create/connect/invite/whatever regardless of which client you (or any of the other participants) happens to be using. The channels themselves are not hosted or even facilitated by the client in any way, shape, or form.
As far as I know most (if not all) servers hosted by the "big" IRC cooperatives (EFNET, DALNET, UNDERNET, etc.) allow private channels by default. The same is true of most lesser-known IRC cooperatives - at least the ones I'm familiar with.
If you tell me which IRC server you're using I can probably tell you whether it supports user-created private channels or not - and there's a very high probability that it does.
And feel free to ask more questions if I just made things more confusing instead of less
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Quick edit: I almost forgot that some IRC clients do support subsets of the DCC family of protocols. DCC can be used to set up limited peer-to-peer (i.e. not server-relayed) chat groups if all clients support the proper functions. To quote ancient cartographers: Here there be dragons
. In other words, not for the faint of heart.