Schwinn Suburban

keep it the way it is.
it'll ruin it's integrity.

Add a front fender or take the rear one off it looks odd.

I'd leave it be. Those things are supposedly kinda hard to find in good condition, and probably wouldn't make the best fixie anyway. I had one, but gave it to a friend because I had too many bikes. For more fixie discouragement go to the Heritage Forums on the Schwinn site. Honestly though, they will have parts and advice galore. What year is it??