Just a quick question, could I use the SHIELD team ability to give a character of 0 range a range of 1?

Second question, does the SHIELD team ability stack, so I could give a character a 3 range instead of 0?

yes to both. Though having a 1 range won't do you much good.

Edit: I'm assuming that you are using at least 3 shield TA's to get the +3 to range.

Unless you're a sharpshooter!

Yes to both questions.

There is no general rule stating you cannot modify a combat value of 0 above 0, and multiple SHIELD team members can boost 1 characters range up any number of times (capped by the Rule of 3, of course).

You could do this to shoot someone in a square next to a square you occupy that is on different elevation. Useful if you don't have leap/climb or such, and can surprise the heck out of someone.

If they make a sharpshooter with zero range, I'm going to smack somebody. Though I guess you could perplex down someones range from 3 to zero and then SHIELD it up to 1 or 3

Or Zombie Spider-Man!

The Elite Sniper feat can make any 0 range Super Senses figure a Sharpshooter.
Having EE doesn't automatically allow him to make ranged attacks.