Investing into a fixed bike Well, two weeks ago I bought this fixed-gear bike and although it was my first time buying one of its kind, I considered it was cheap.

Problem here is that when I tried to search for any clue of the brand... oh surprise, there's no brand!

I was told that it was a pure cycle fixed bike, but I realized that it was painted over and the only thing that I have is a serial number that throws no information when I search it on the web. 

Should I invest my money in add the front brake? And also all of the details that it has? (Bad paint job, change relatively new wheels, fight the rust that is forming in the gear?)

I paid $80 USD. And I bought it mostly because I wanted to have a fixed bike and to start learning to repair bikes. Could I sell it for more than the final price that will cost to me?
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!