Let's start with the simple one.For the LEDs you will need resistors - 120? to 150? should be fine (R=V/I = (5 - 2. / 0.02).As for the chip, all that does is convert the 0-5V of the arduino to the 0-3.3V that the display needs. You can achieve the same result in a large number of ways, not all requiring a chip.For low-speed communications resistors arranged in "potential dividers" can be used. For higher speed you can use diodes, transistors, any number of methods.
You might find this video by Jeri Ellsworth helpful.http://www.youtube.com/watch?v=XNIpvop0ruI&featureHave you thought about using a voltage divider if you're going from 5v to 3v3 in one direction?