What causes extra swaps?
Solution 1:
When you make a combination of 5 or more gems of the same colour you will get an extra swap.
Swapping 3 green and 3 red in a single move will not get you an extra swap.
As for the chaining: I have asked support whether it is possible, but I believe it will be. Although it will be hard to get a chain since it requires 5 or more gems from the same colour.