No, they don't get drunk but when they have a tummy full of nectar, they become quite docile. If you see one that looks wobbly it may just be dying or ill - an individual bee may not live very long, and some get diseases. All the male drones get pushed out of the hive to die off at the end of the season. I'm not sure if they actually sleep in the way we do.
Although they can go seven miles, they dont't normally go more than two or three miles from the hive - they'll go for whatever is nearest and most abundant in nectar. If they find any oil-seed rape, they will happily pig out on that and not look any further.
The popular plants with bees in our garden at the moment are various cotoneasters, sage, and the perennial geraniums (cranesbill-type). They bees are practically queuing up to get at the geraniums. The thing I really must get is a flowering shrub called abelia (there's a clue in the name) which bees really love.