No, that wouldn't make any sense. General Calrissian gave the order for all ships to pull up, as he realized the shield was still up. Logically, the only reason to pull up is if they would be destroyed trying to pass through the shield (or the rebels could just go straight for the Death Star openings to fly towards the core). The star destroyers, including the SSD Executor, are all behind the Rebel fleet, and thus outside the area shielded by the generator on Endor. They can only be defended by their own shields, not the planetary shield projected from Endor.
Your last part is probably right, the dome was blown up likely to demonstrate that the ship's shields were down, but the explosion followed by the dialogue lead to the belief that the domes were the (ship's) shield generators. Which was later made true.
Ayep. Haven't looked at any of the schematic or cutaway books in years, though, so they may have changed the belly bubble to something else entirely and gone ahead with the domes for all shielding, just each dome doing different parts of the ship. I dunno.