Investing into a fixed bike
Yes, add the brake - as others have said, it might not be 'cool' but you'll end up being much more confident on it knowing you can stop it quickly. I also can't work out if you have foot retention or not from the picture, but even with a brake I'd highly recommend some kind of foot retention, and if you ride brakeless you are pretty much unable to stop at all without it. 
If you like it and it fits, keep it. If you don't really like it, or it doesn't fit then it doesn't sound like you'll lose too much by selling it. 


I'd get a brake on it and make sure it's serviceable then ride it for a while and see how you like it. Riding fixed takes some getting used to, so get some miles in before making your mind up!