Brian (Anti Zuckerberg)

Attack speed doesn't increase damage, it increases... attack speed.

Spawning an item with specified attributes will cause it to only have the attributes you gave it. This means spawning a sword with only attack speed will make it not have a damage modifier because you didn't give it one.

That's because of the animation it uses. If you pay attention, your hand/whatever item you swing will rise back to it's typical resting position as the attack cools down. If you set it to 0, it'll never cool down, causing the hand/item to never rise back.

Hoppers can not pick up an item 2 blocks above them. Items need to be within one block to get picked up. If a block above a hopper is less than one block tall, the hopper can pick up items.

That hopper is working perfectly fine. The redstone torch is powering it which locks the hopper from moving items. Other hoppers can put items into a locked hopper, but a locked hopper can't pick up or push items.