Powering an Arduino Uno

michael_x:
I guess you'll see a voltage drop of 2.5 V at each led and a current of less than 20 mA. No resistor required, probably.

I can't agree with this point. The resistors with LEDs are required to limit current. You can't omit them if you have a lot of LEDs.

Read this:

http://www.thebox.myzen.co.uk/Tutorial/LEDs.html

In there he says:

There are several web sites and schematics on the web that suggest you can attach an LED directly to an Arduino output pin with no current limiting resistor. They are wrong, and following them will damage your Arduino.

Is this true? In this case, will 5V not be enough to handle my two 3.3V LEDs in series pairs?

Do the LEDs really have a 3.3V forward voltage? In that case you are limited to one per pin. I think some external circuitry is starting to look good here.

Bonus question: As long as only one LED is on at once, I could handle driving all 14 seperately, right?

Yes that should be OK. Still have to keep the current within limits for the pin (eg. 20 mA).