Yes, gangs exist, even in the most unlikeliest of places. You may find that depending on the area, the community may deny their existence. Police reports aren't always a precise indicator either, as some will not report activity for worry of stigmatizing a community. It's best to walk the community, ask neighbors, visit local shops...get a feel for the area. It's about your subjective opinion as to whether you feel safe in any area. Don't be lulled into a false sense that one neighborhood is safer than another...for that's when you may let you're guard down and become a victim.
With any city, gangs are an unfortunate reality. That said, it is a very small segment of the population and is rarely a problem. We lived in the heart of Denver for 12 years and besides spotting an occasional tag (graffiti), we never experienced any problems. Overall, Denver is a very safe (and fun) city to live in.
Yes, but they are in a rather small section of Denver and most of the violence and general mayhem they cause is to their rival gangs. If you stay in the nicer areas of Denver, you rarely hear about them.