Questions on Tiptronic S (2006 Cayman S) - The Porsche Cayman Forum

Hi everyone,
Last week I decided to become a Porsche owner and got myself a mint condition Speed Yellow 2006 Cayman S. While my other car has manual gear box, this Cayman S has a Tiptronic S. I have the following questions I hope someone as experienced Tiptronic drivers can help to give me some understanding:
1. I found the gear change responsive when using +/-, but when it was in "D", and when I was gently driving off, it changed to 5th gear so quickly it was only doing 50kph plus (which was only about 30mph). When I was accelerating hard, it was much better and managed to keep itself at the right gears long enough to push acceleration. Is this the intended characteristic of a Tipronic S?
2. In "D", approaching a roundabout in relatively high speed, brake brake brake, gear down shifted to "2", before turning stepped on it, nothing happened as if it was on 5th, but indicator on dash board showed "2". Just when it headed straight, throttle response came back and the car shot like an arrow down the road. I did not lift the accelerator, but the revs just came back as soon as the turn was over. Was the PSM in action? If I understand correctly PSM works as Traction Control, and it influences throttle response, braking and revs. Kindly advise if I was wrong.
3. Steering all the way to either left or right, drive off gently in "D", and gear changed to 1st. As it headed straight, gear changed to 2nd, 3rd so on. If I did not lift the accelerator, I would have to change momentarily using "+". What was happening? I could not simulate this when I tried purposely. But it just happened a few times by itself.

Other than these, the car is just brillient. I would be most grateful if anyone here could help me on these.

Thank you very much.