I just got an Amazo and I had a thought about his Hypersonic attack. Could he use the dumpster repeatedly while making a HSS attack thus making for multiple 3 click attacks?

Once you use the dumpster you drop it. Of course you can use the hit and run to pick it back up.

No. He can use the dumpster on the first attack but once it is used it is taken away from him and placed on the map. So you could get the bonus from it for the first attack but not the others.

No because once you use the dumpster once, it is out of your hands and is placed adjacent to the enemy fig. Now, to pick up an item requires a move action but using the HSS 'rapid punches' attack you cannot interupt that.
As I understand it, you could use the dumpster on the first attack (reduces your damage to 1, but then +2 for heavy object), opponent then places dumpster, and you continue to roll (-1 to hit / attack) doing 1 damage for each subsequent hit.

Actually, the player who uses the dumpster gets to place it after it is used.

And keep in mind---to use the Dumpster at all, you will have had to pick it up on an earlier turn.