Connecting the motors to the wheels is one of the trickier parts. I got a few Lego Technic pins and replaced the hind axle, which is a "Crossaxle 3M with Stud", with a "Cross Axle 2M with Snap".

Connect the motor shaft with the Lego axle by wrapping a bit of tissue around the shaft until it fills the Snap bit. Then soak the tissue in super glue and stick everything together quickly. I actually used band-aid instead of a tissue and it worked quite well. There are other methods to do this, just google "connect DC motor to Lego".

Also, because this axle is 1M shorter, you need to take out the "1/2 Bush" part to fit the wheels back on.

I hope this made things clear. Good luck with the project!

Sure you can use the Uno, I don't think that would be a problem. I mainly chose the Nano because it is smaller.
Feel free to use it for your school project and let me know how it goes! :-)
You might be lucky and someone already uploaded a 3D file with Wall-E somewhere for you to re-use!

Generally speaking, yes. But in this case, the infrared sensor just fits in better with his appearance. The standard ultrasonic sensors always have a fixed layout that doesn't work with the shape of his eyes. That's why I chose the infrared sensor for this project.