I am not sure if you are aware, but water will expand roughly 8% when frozen. This is another way of saying that the area water takes up will decrease by roughly 8% when it melts (when it is no longer frozen).
It's actually closer to 9%. Regardless, sea levels will rise because the majority of the ice is not currently in the sea, but above it. When it all melts, sea levels will rise by around 70 meters.
I am not sure what that picture is of, perhaps of an ice cap on land. The density of ice results in approximately 92% of it being under water.
The assertion that all of the world's ice will melt seems like fear mongering to me.
Classical fear mongering, and not even supported by radical environmentalists.
The North Pole ice is floating, but Greenland is two miles of ice on top of land. Antartica is ice on top of land, with the arguable exception of the western peninsula. Obviously ice on land is not even influenced by warming or changing ocean currents.
Now for the meteorology. Temperatures on Earth go DOWN as you go UP in altitude. About 3C per 1000'. So if you go up 10000 feet, it's much, much colder. Now think about the effect of that in polar regions, where it's already very cold due to little sunlight.
Arguments that Greenland and Antarctica will melt are simply unscientific.