1 gallon = 4 quarters.
about 250 lbs.
20 i think
A really, really large number. (But more than 2.5 times as many dimes would fit in the same barrel -- so if you're offered a barrel full of either dimes or quarters, pick dimes.)
500 or so pounds.
It depends on how well they are crushed.
A quarter is 808.5 mm3. If you melted the quarters into a slurry, and poured that into the barrel, you could fit 208 million/808.5 = 257,000 quarters into a 55 gallon drum. If you want to preserve them whole, this becomes a stacking problem. There will be spaces between the quarters, and we would have to estimate how much space is wasted. Just drawing packed circles on a piece of paper I'd guess perhaps 10% of the volume would be air, so deducting 25,000 quarters from our solid mass gives a ballpark estimate of 225,000 quarters.