There are no physical signs of construction. They are still working on getting permits.
KIAC, the corporation that runs the airport, says they are still shooting for a 2007 opening for the second runway.
In his year-end comments (Dec.1998), the president of KIAC said they expect to soon finish up negotiations with the fishing industry, which would allow them to get the permit for filling in the ocean to make the second runway.
He says they are still committed to starting construction before the end of 1999.
The runway will be on the far side of the current runway and parallel to it. The airport itself is 5 kms off the coast. There is no need for a perpendicular runway (as is seen in some old illustrations), because any winds that would necessitate one would shut down the 5 km rail and highway link, thus cancelling flights anyway.
The new runway will have:
4,000 m runway
180,000 t/o and landings per year
To answer your second question about sinking:
I have not heard anything about this since the big earthquake in Kobe a few years ago. As you probably know, the airport buildings are on adjustable jacks to compensate for subsidence. (You can see the jacks on the ground floor of the parking garage.) The roads, the runway, etc., do not seem to be subsiding, however. There are other manmade islands in Osaka that are very obviously sinking--the roads have waves. But so far no such signs at Kansai Airport.