When you legally buy a handgun in the US,are you allowed to carry it with you or you have to keep it at home?
Does every citizen have the right to buy one?
I know these things vary somewhat from state to state....
But generally?
As long as you don't have a criminal record, noted substance abuse problem, or have been committed for mental illness reasons, you'd be able to buy a standard rifle, shotgun, or handgun. Here is the standard form you fill out at a gun shop -
http://www.atf.gov/file/61446/download . There are other rules for things like machine guns, Sawed off rifles/shotguns, etc.....
As you noted certain states, usually in the upper mid-Atlantic, lower New England make it harder. Also California, Hawaii, Chicago, Washington DC.
Right to carry is a sticky topic, but it is generally pretty easy in most states to get a CCW permit. Some states, about 60% of the country, allow open carry (must be showing gun in open view) with no permit. A few allow both concealed and open with no permit, and most allow it if you have a permit valid in another state.
