Hi Vinay,
I think you need to be careful here. Simply moving the inductor in one direction or another may reduce one effect and increase another. As much as possible you should try and isolate the effects. I suggest the following.
1) split up your layout into a few sections. The Ld network, the Lg network, the Ls network, and the transistors.
2) extract the individual networks one by one and gradually replace the ideal components with extracted ones.
3) finally add all components into one layout. This will reveal any coupling.
Regarding your other questions.
1) To get higher inductor Q, you need to design the inductors yourself.
2) Up to you. To me there are four possibilities.
a) There is some impedance transformation. But looking at the trace lengths and the sizes of your inductors, I doubt this would have such a great effect. If I remember correctly, impedance transformation wouldn't change the "available" power at the output, so you can look at that to verify.
b) Your inductors are being de-Q'd. Make sure there are no large closed metal loops as these will kill your inductor Q. Especially in the ground shields.
c) There is some feedback. Coupling between your inductors could result in feedback which would reduce your gain.
d) There is a problem with your extraction. Try using an EM simulator for the inductors and traces.
3) I made a slight mistake here. Increasing that line would indeed increase Ld, but not so effectively, as the mutual inductance between Ld and the OUT-Ld trace appears to be negative in your case. This is not good because it lowers the Q of the inductors. If Ld turns in the opposite direction, you should be able to get even higher inductance and better Q. But because the trace is small, the effect may also be small.
4) Make sure there are no closed loops in the ground shields. I'm sure you've heard of eddy currents...
5) VDD and GND are both considered to be AC ground. At AC they should be the same net, and so its good to have strong coupling between them. That's the general rule anyway...
6) There definitely appears to be a loop in between the three inductors formed by the connections between the ground shields. I cannot stress enough how amazing this book is,
http://www.amazon.com/Signal-Power-Integrity-Simplified-2nd/dp/0132349795/ref=la...its by Eric Bogatin and its called Signal and Power Integrity Simplified. It will answer all of your questions for you and everybody will think you're half man, half amazing
7) I'm not really sure about the difference between Calibre and Assura. For L and K extraction I've only used EM simulators.
cheers,
Aaron