Why does my new floodlight trip the circuit breaker?
The green/ground should be connected. My understanding (others more expert will correct me if I'm wrong) is that if the box for the floodlight is metal and has metal conduit going back to the switch, etc. then the box should be grounded and that the normal thing to do without a ground wire coming in to the box is to connect the floodlight ground wire to the metal box. If the box is NOT grounded that wouldn't hurt anything (but would NOT be providing the expected ground, but no worse than a capped ground wire, which does no good at all and is most likely not considered a complete/proper installation). But if the box is somehow hot then (a) you have a dangerous situation and (b) every time you touch the case of the floodlight (which should be connected to the floodlight ground wire internally) to the metal box you will trip the circuit. So I see two likely scenarios:

1 - Floodlight is good. Box is bad (shorted to hot?). Need to diagnosis/fix box problem, which may be a bit complicated. Check for voltage between neutral and metal box - should be 0 V, if I understand the nature of neutral/ground bond correctly. If it is 120 V (or anything more than a few V) then I think either your metal box is hot (VERY bad) or hot/neutral reversed somewhere (also VERY bad) - figuring out which one would require a bit of detective work - but definitely need to fix before installing the light. I just noticed you DID test neutral/box = 0 V and hot/box = 110 V, so that would indicate the box is OK (though unknown whether it is a proper ground or not) which leads to...

2 - Floodlight is bad. With the floodlight disconnected from the circuit, use a tester to check for continuity (or low resistance) between (a) ground wire and metal case - (good), (b) hot wire and metal case (VERY bad), (c) neutral wire and metal case (bad, but if I understand things correctly, that shouldn't cause a sparks-flying-breaker-trip). If (b) or (c) then I think you have a defective floodlight.