If you watch carefully, the Ughnaughts (little pig guys) remove Han's cuffs right before he goes into the chamber. Of course iirc, the white shirt he's wearing during that entire scene is different than the one he's wearing in the Tatooine scenes of ROTJ... so there's still a continuity flub between the films.

The Hoth shield thing makes perfect sense in light of the prequels (Episode I, actually). A theater shield stops projectiles, energy, and fast moving objects, but slow moving metal objects (walkers) can push through. The Hoth shield is like the Gungan theater shield only much, much larger (protecting a portion of the planet, so it could be many kilometers in coverage... the walkers would have to land outside the shield and push through, then scurry on to the base to attack it). Sure, I suppose the Star Destroyers could have bombarded the planet (not the shield) and turn it into a steaming ocean, but Vader wanted Skywalker captured alive.