LED Questions

Help, I'm afflicted with inspiration in quantities that exceed my skills!

So I came up with an idea for a project that would probably require the use of LEDs, which I know next to nothing about. Ah, said I, the Internet can teach me much... so I turned here and found the (nearly) perfect Instructable, "LEDs for Beginners":

http://www.instructables.com/id/LEDs-for-Beginners/

Having read this most helpful I'ble, I certainly came away more knowledge than I'd previously had, but still not enough to properly plan my project.

Basically, I'd like to create a 2D "array" of LEDs to use as a light source, in order to backlight a roughly 8.5" x 11" translucent panel.

It seems like it would be straightforward to just wire up a bunch of white LEDs in series to a power source and a resistor, and be done. I'm not afraid of a little trial-and-error, but I prefer to know at least roughly what I'm doing going in, so I'm asking for your help. Here are my lingering questions:

1. Should I wire my LEDs in series, or in parallel? (Or some combination thereof)? In series, I gather that one LED failing will break the whole circuit, which could be a pain. On the other hand, I've seen several projects and sites that cryptically recommend against wiring these in parallel.

2. Are there pre-built strips of LEDs I could acquire that would make this project simpler?

3. If I want to vary the brightness of my light source, can I use a variable resistor (potentiometer), or does the nature of the LEDs preclude the use of this type of dimmer switch? If so, could I vary the brightness with multiple switched circuits, turning off half the LEDs for half brightness, 3/4 off for quarter-brightness, etc?

4. I've got a slew of transformers from old tape decks, telephones, cell phone chargers, etc. Can I appropriate one of these as my DC power supply?

5. How do I gauge how many LEDs I'll need, and what density is best to lay them out? I'm looking to create even, diffuse light, with no noticible bright/dark spots.

6. Do I need to worry about heat?

7. Are LEDs even the correct way to go here? Should I consider fluorescent light instead?

I realize these are a lot of questions, but if you're an expert on LED projects, you could save me a lot of research time. If (I build this gadget, it will definitely show up here as its own Instructable.)

Thanks!
-JD