1) The command is, very simply, "/nick <name here>" (without brackets). So, for example, if I joined an IRC channel or server and wanted my nickname to be "LoganK", I'd type this:
/nick LoganK
And the server will respond with either a success message (you got the nickname) or a failure message (either it's protected, someone else is currently using it, you have incorrect syntax or illegal characters, etc.).
2) I only used Trillian for one day before I got fed up with it. A few months later, I tried it out again and used some...um...programs to <cough> "fix" </cough> it to the pro version. Unfortunately, the pro version annoyed me just as much as the basic. It wouldn't remember my accounts (for example, I have all my accounts set-up - then I come back a few hours later, after losing internet, and my accounts aren't even there anymore!). It also would not work with some of the proxies I use, and, upon trying to change the AIM login server to something different, it worked on one of the many networks I visit everyday but not my other networks. Now I use Gaim and couldn't be any happier. IRC, AIM, Jabber, MSN, Yahoo!, ICQ, and a whole host of other networks I've never even heard of are all supported by Gaim, and: it's free, the source-code is available, and there's plenty of extensions. To answer your question (because I've just typed a whole paragraph of irrelevant nonsense), I don't know how you can use IRC with Trillian. Just setup an account like you would normally, select IRC as the protocl, type in a server name and channel, and I assume it'll open up the channel in a window or add it to a buddy list...in any case, searching on the Trillian help sites / forums may help you out a bit more.