Without googling for it my understanding is that they are more in tune with nature and the world around us, the season and good harvest etc. Rather than having one God they pray to various Gods that effect natural forces such as weather etc to bring good crops, fertility and the such like.
the word is sometimes just used to mean non-Christians, which would include druids, devil worshippers (like your tenants) and Muslims. But these days it's more likely to imply nature worship
well, it could be, though I think that heathen is mostly a Christian term for non-believers generally - probably not Jews or Muslims, but perhaps Hindus, Sikhs and Buddhists. It's a slightly derogatory word; pagan is more neutral... I think, but others may use the words differently. I'm not sure any of these terms has a guaranteed precise meaning.
The term pagan comes from the roman word 'paganus' meaning country bumpkin. Christianity was the religion of the richer town-dwellers while the country folk carried on as they had for centuries. When christianity became the offical religion country folk remained off-message - hence, pagans.