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So lots of it is below sea levels. Same for Iceland?/Greenalnd. So all that which is below sea level will NOT raise sea level when it melts.
And yes, ice shelves and ice bergs are already displacing sea water, so will not raise sea level when they melt either. DIY experiment: fill a glass with ice water, let it melt. see if the level changes.
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You seem to have a misconception here.
Only ice that melts
while floating on the sea does not change sea level. Any ice that melts, and joins the ocean, that did not float on the sea increases absolutely the volume of sea water and contributes to rising sea levels.
If ice melts below sea level under an ice cover that extends far above sea level cannot carry the weight above it will try to find cracks and channels to be pressed upwards. If it finds the sea that way somehow, sea levels rise.
Now of course rising atmospheric temperatures will first affect the surface ice, not the ice 2 km below the surface. The surface ice does indeed flow towards the sea, where it melts and contributes to rising sea levels; this ice is called "glaciers". This happens all the time, and has been happening all the time evers since Antarctica had an ice sheet. This loss of ice is of course countered by snow that falls onto and adds to the ice - which had previously evaporated from the ocean and decreased sea level. There is, ideally, a dynamic equilibrium between snow falling on Antarctiva, and sweet water glaciers melting into the ocean.
The question then is: How does global warming affect both sides of this equilibrium? Do glaciers flow faster downhill when they warm up? Will more or less snow fall onto the continent? You have questioned a couple of times that the inland ice won't just melt, because it is still freezing cold. You are right - it doesn't matter so much if -15 °C or -10°C, both are freezing, not melting temperatures. But a) Some parts of Antarctica do see >0 °C some time of the year, and that might increase both in area and in days/year; and b) It's really the flow of sweet-water glaiciers that you need to look into.
All that equilibrium is pretty unaffected by how deep parts of the ice sheets reach under sea level, as long as they sit on rock rather than swim on sea water.