Q31: armour width depends on the volume of your ship, ie it's total tonnage. Higher tonnage, larger volume, bigger ship - more armour width. This just means there are more locations for weapons to hit. Depth is the actual thickness of armour and is the part that really protects the ship. Different weapons deal damage in different formations - for example, lasers make deep gauges that are very narrow, so if the first hit does not penetrate armour, it's highly unlikely to get a hit in the exact same spot again. Missiles, OTOH, create craters, so it's easier to get a second hit on or near the first hit, which helps overall armour penetration. In essence, you need to "sandpaper" the armour away before you get to inside to do some real damage. Check wiki for the exact damage variations of different weapons, it's all listed there.
Q32: No, the resolution means the size of a ship that the sensor is optimized for. It will detect smaller ships but not on the same distance - so smaller ships can sneak closer to your sensor before it picks them up. IRL, a larger ship would be spotted farther away than the nominal sensor range (to a degree), but I think that Aurora has it capped to the nominal size. So sensor with 50HS resolution with the range of 20 milkliks will spot anything bigger at the same distance but smaller objects would get closer.
