Pigeons are good with a shottie and its rare you'll find any shot in the meat, but IMHO, I'd recommend an air gun or rimmie to head shoot rabbits if you're eating them - shotguns can mean a punctured gut on a bunny which isn't too nice.
I shoot pigeons out to 50 yards with my 12 bore very successfully.
No, you definitely don't need land to anchor a shotgun cert to.