I don't have any personal experience with the mask, but I recently heard a podcast on the subject of respiratory training devices. The guest was Greg Wells, Ph.D., who spoke about a couple of these products. Here's a link to the podcast: Ben Greenfield Fitness: How to Increase your V02 max
The podcast will probably answer most of your questions in more detail, but here's a brief answer for each:
The altitude mask does not create the same physiological response that training at altitude does, because it does not reduce the %O2 in the air you're breathing (which is what causes mitochondrial development and other adaptations to altitude training). Instead it restricts the flow of air into your lungs. That said, preliminary studies have shown that resistance devices like this can provide performance benefits by making your diaphragm stronger.
These benefits are relevant to all athletes, but are especially beneficial to middle-distance athletes such as 5k-10k runners. Interestingly, the Powerlung (one of the first devices in this category) was originally invented for rehab purposes, and was later discovered by athletes.
You should begin by practicing breathing through the device (mask or Powerlung) in short intervals throughout the day. Like any new exercise, your body will take time to adjust. Training masks should only be worn for short workouts at first, and then you can increase the duration over time. The Powerlung devices have variable resistance settings, so you should start easy and slowly increase the resistance as your lungs develop.
I don't recall hearing of any negative side effects, beyond the dizziness that might happen at first. Of course, if you really overexerted yourself, you could faint, but this is not unique to respiratory training devices.
As for research, there was one study linked in the podcast's show notes. You can also read a digest on Greg Wells' website: To Breathe or Not to Breathe. This references a few other studies as well.