Firefox - Browser.
Thunderbird - Email client.
Platform - Mozilla platform, also known as Gecko. Standalone version is XULRunner.
XUL - XML User interface Language.
1. What are nightlies?
Nightlies are nightly builds produced by the official build machines. They comprise of the latest code in the official repositories as of a fixed time every day.
2. Where can I find changes that occur in nightlies?
The Burning Edge summarizes some of the weekly changes to Firefox, while The Rumbling Edge does the same for Thunderbird. Calendar Weblog lists Calendar changes, and SeaMonkey Trunk Tracker is the corresponding one for SeaMonkey.
3. Where can I download nightlies?
4. Where can I see the latest build statuses?
Tinderbox is a good start.
1. Which are the common IRC clients?
A list can be found at Wikipedia - List of IRC clients. Find one that works on your platform. Recommended ones are Chatzilla (cross-platform), irssi and Colloquy (Mac).
2. Which IRC channels do I ask for help?
Head to #nus first, where other members of the Mozilla community in NUS can try and help you. If not, head to #firefox or #thunderbird, whichever is relevant. Finally, your last resort is #developers, or #maildev for Thunderbird issues.
3. What are useful tools to complement IRC?
Pasting large chunks of code in IRC channels usually does not make it easily readable. Pastebin is a suitable for such a task, while TinyURL is suitable for down-sizing very long URLs.