I thought that melting of the polar ice cap would not result in higher sea levels. The ice floates and thus takes the same amount of space as the melted ice (Archimedes). Am I wrong?
No.
Removal of floating sea ice will not impact sea level but will change the albedo and result in greater warming.

There is the danger of futher positive amplification of this warming trend due to the release of GHG from the once frozen arctic tundra.

The Greenland ice cap is not floating. Scientific opinion is changing with regard to impacts. It was believed that increased warming would result in increased snowfall and sequestration of water in the Greenland ice cap. Current data shows continued abalation of the ice cap and glaciation retreat. This would contribute to significant sea level rise.

The ice above the water line is displacing its own weight in water. Consequently when it melts there will be no change in levels.

Likewise the albedo thing doesn't seem the major issue; the poles are very cloudy anyway.

I expect the real positive feedback is in the changing ratio of surface area to mass of the ice as it melts. Surface area decreases with the square, mass with the cube (pardon!), so the less ice, the faster it retreats. I suppose this is why we're seeing so much greater warming at the poles.

I suppose then the problem is the loss of heat sink. The phase change of melting ice soaks up a lot of heat. As the ice shrinks that sink goes away.

To dramatize this my old physics teacher would set a paper cup full of water on top of a bunsen burner. The cup sits there happily ignoring the blue flame underneath it right up to the point that the last of its contents is gone. Then it ignites.

So we may expect that more equatorial regions of the globe won't experience the full effect of warming until the polar ice is gone. At which point ... well, I'm too busy moving to Tasmania to think about it.

I'm from Tasmania, Why move there?  

I would it expect it to suffer severly from changes to the Antartic.

It is not just the Artic that is changing