I'm sure there's a good way to get the connector off the battery, but I basically just tear them open with pliers. You can try taking off the LED, then ripping out the battery, then peeling the metal off like a banana (that's generally what I do). Others have suggested using pliers to crimp the metal about an inch down from the connector, then crimp it at 90 degrees to the first, then soak it in hot water, attach an atomizer, and gently rock it back and forth until it comes loose. Never done that one, though, so I can't say how well it works. At the end of the day, just find a way to get the connector off without scratching the threads or puncturing the battery.
As to you other question about the positive and negative battery connections, they are not connected. If you look closely, you will see the positive connection in the center is separated from the negative connection on the outside by a thin piece of non-conductive, rubbery material.