Some features are not immediately obvious.
You can make a window transparent, like a WoW guild chat, by clicking the little circle. (Like in the screenshot).
There is an anti-spam feature which makes you pay a few ISK to invite someone to a gang or message them. It's the "CSPA" charge. You turn it off in a hidden area.
In your inbox, you right click on the little 'inbox' wording. This brings up a menu including Settings. In there, you can add your Corp or Alliance to a list of allowed people.
If you have drones, you will find a variety of right-click options on the drone window below the Overview. You can send all your drones in to fight at once this way.
It's worth right-clicking on windows and objects just to see what's hidden.
Lastly, there are no addons that customise your GUI, sadly. Many MMOs have it. Eve doesn't (yet, perhaps, we hope).
Yes, they exist, and they're just as important for PvP in Eve as they are in Warcraft. They're not as configurable, but are accessed by hitting your escape key to get the control panel.
Stop ship moving: CTRL-SPACEBAR
Target a ship: CTRL-CLICK
FPS, frames/sec: CTRL-ALT-SHIFT-M
To increase FPS
General effects on/off: CTRL-ALT-SHIFT-E
Turret effects on/off: CTRL-ALT-SHIFT-T
Sound on/off: CTRL-ALT-SHIFT-F12
The Rookie channel you activate during the tutorial does not stay closed; it re-activates itself. It's annoying. You can't get rid of it until you've played for 30 days.