It is a miniseries…..
No. It is an anthology series and some theories have stated that the seasons might share a small connection.
Yeah, Ryan Murphy confirmed that they're all connected apparently.
The miniseries/movie category in the Emmy's have been a little strange, especially lately; British TV series such as Luther and Sherlock have made their way into those categories in spite of their being ongoing shows that should be under Drama, and Fargo, like American Horror Story, is another "miniseries" that's getting a second season. Meanwhile, True Detective was pushed by HBO into Drama instead of miniseries in spite of being similar in approach to AHS and Fargo.