Is there anything I can do to increase the power of my turning kick?
Make sure you have the full rotation. For a roundhouse, your standing foot should be close to 90 degrees at the end of the kick. You can check this by going up against a wall and extending your leg out to kick (using wall to balance as needed). When it reaches the full extension, check to see if your standing foot has rotated, along with your hips. As JohnP mentioned, you should be rotating on the ball of your foot.
If you have the technique down, then it's just a matter of building the strength. A simple exercise for this - using the wall again for balance (as needed), hold your leg out at full extension for a certain length - 30 seconds, 1 minute, you decide what works for you. This will help strengthen your leg for kicks of varying heights. As you've probably heard many times - practice, practice, practice.
Does the snapping action results in a loss of power? I think it creates a greater momentum, but not sure whether it adds more damage.
In comparison to a what kind of kick? What is the baseline? A front kick? I feel that would be an unfair comparison, as the usage of a front kick is different from a turning kick. Though, I've mostly seen front kicks used as a "push" to move an opponent away, and less as a power kick/scoring kick in taekwondo. Someone else can provide insight on this?
In taekwondo, the snapping action, I think, is more for recovery in preparation for the next kick(s). With the established rules in the sport of taekwondo, I am under the impression the snapping action is a result of this. Sparring is continuous, and it's usually only as a result of KO headshot that a single kick is enough to end a match. Those are not easy to land. You can still generate a lot of power from the snapping action though, and the key to that would be in rotation and continued practice.
Here's a Fight Science Video that examines the kick style and uses numbers to create some baselines...but I still feel it ultimately comes down to the individual. With continuous practice, and you'll be able use whatever method you learn very well.
Fight Science Video