It clearly says that the Vulture 'drops the manhole cover into place', so that clears that up - he shoves it aside, grabs the diamonds, then pulls into back into place as he leaves. The artwork makes that maneuver look like it must have been a tad complicated, seeing as how the manhole cover probably landed two or three feet to one side of the manhole, which means the Vulture would have to scramble partway out of the hole and drag it back into place - but hey, it's not the first time that Stan's writing and Steve's artwork didn't completely match up.
I'm presuming that the little holes are self-sealing, so that once they've sucked all the air out of the container, they close up, leaving the occupant somewhat short of breath. These guys ARE aliens, after all. (Well, technically they're NOT, due to subsequent retcons, but at the TIME they were supposed to be aliens, and that's the point.)
I'm guessing that the crooks have a truck or something parked around the corner where we can't see it - they do, after all, appear to be in the middle of the heist, so one may surmise that they don't plan on lugging that thing any further than they have to. (Well, either that, or they're planning to shove a false exterior over it, and disguise the thing as a hotdog cart.)