They prefer to be on water, as there legs to body ratio is a bit off, but as mentioned do , do well walking around.
As for imprinting, yes, they will if you hatch them or get them very young, they are quite docile birds, not nearly as aggressive as geese.
Cant speak for state to state laws, GA has no such law as yall have mentioned.
Federal laws cover all north American migratory species of water fowl, of which the mute swan is not I dont believe, whoopers, tundras, whistlers, ect are. I know they have to be either toe clipped or pinioned, this is not to prevent escape into the wild, but to verify they are captive raised and not wild caught (which is highly illegal).
Any of these birds will come with the proper permit and paper work, IF you are buying from a legal breeder, and that will be all you have to have, unless you plan to breed and sell as well, in which case you would then need to contact the U.S.D.I. and get your own Federal Migratory Waterfowl Breeders License in order to legally sell them, this would be when you have to keep records of ALL eggs, births, deaths, sell, ect for you annual report to the U.S.D.I.
Like I said, this is Federal, each state may be different, I have never heard of such state laws, but it would bare checking into to be safe, as they can get picky over waterfowl!!