A picture of the faucet may help. But from the looks of it the faucet is removed from the top of the sink a the faucet drops out from below. The nuts your looking at from below are used to adjust the faucet height through the sink surface.
Remove the two cover plates. That would allow the faucet to drop down through the sink except for the spout will also be holding it in place. Your first picture didn't show the under side of the spout. Some had a allen screw were the pop up rod went through the spout that held the spout in place. Others have a nut under the sink on the spout that has to be removed.