Terraria – How much of an underground area must be removed and rebuilt to stop mobs from spawning

With the Clentaminator present in the game, this is actually quite easy, if a bit time consuming and expensive. Dig hellevators every 120 blocks across the area you want to purify. With the Green Solution equipped, float down the each hellevator twice, first spraying to the left, then to the right. I recently did this in one of my worlds, and it worked perfectly. I'd recommend checking every so often after you're done to make sure you didn't miss anything. This will also turn any underground mushroom biome to jungle, so you may want to go back when you're done and convert it back with Dark Blue Solution.

When I did this, I left large swathes of land from the surface to the underworld converted, and even brought in Crimson from another world so I had all the biomes present. Just make sure that if you do this you put wider shafts (I left six blocks) around the corrupted/crimsoned/hallowed areas so they don't spread.

The simplest way? Cover the moat with a layer of dirt in the short term.

The "this is awesome" way"? Build a "draw bridge". This requires access to the engineer. This is a guide on the official forums explaining how. The video is excellent; he narrates exactly what he has done and even uses annotations in the video to make sure you understand what's going on.

the drawbridge can be toggled via switch. When it's "on", there's a path. When you turn it off, the blocks are not active and so it's open air. Toggle it on when you're waiting for an NPC to spawn and then back off again once they're all moved in.