Yes, definitely, absolutely. The amount of time, effort, and consideration given to the supernatural by pre-modern Europeans is astounding, and consistent well into the 16th and 17th centuries. A wonderful source for discussion on this topic is Peasant Fires: The Drummer of Niklashausen, by Richard Wunderli.

The supernatural shaped the basic understanding of time and space for pre-modern (and, if you do not discount religion, most modern) people. Not accepting the primacy of empirical materialism, but still keenly interested in understanding how the world around them functions (as nearly every human is), the explanatory faculties of Europeans clung to the traditions and systems of their ancestors. These traditions involved strange creatures, entities, and forces which ranged from mysterious to friendly to terrifying.

What's most important to remember is that, as far as anyone was concerned, this supernatural understanding of the universe worked, and was the best (and often the only) way to understanding natural phenomena, social structures, and twists of fate.

An example, from Natalie Davis' The Return of Martin Guerre: the you son of a rich peasant family, Martin Guerre, marries his equally young wife. After several years of marriage, no heirs are produced, leading the village to mock Martin roundly and leaving his family's future in limbo. Now, the modern mind might leap to the conclusion that Martin or his wife were physically infertile, or perhaps that Martin was too young and nervous to physically complete the deed. However, to the mind of his father and the other villages, something supernatural was clearly intervening and preventing his son from producing an heir. In light of this understanding, the parish priest and a wise old widow together perform a ritual upon the couple, who are tied on opposite sides of a supporting beam of the house, in their bedroom. The ritual involves utterings of sacred words from the priest, and spells meant to ward off evil spirits and creatures by the wise woman.

Immediately after this ceremony, Martin's wife becomes pregnant and, nine months later, gives birth to a healthy young boy, now the heir to the Guerre name and fortune. As far as anyone, even ourselves as modern observers, can discern, the ritual simply worked! Some evil spirit had entered Martin's body and kept him infertile. Now, thanks to the ritual, he was free of the spirit's influence. And this was in the sixteenth century!

The point being: sane adults really believed in "all that stuff" because, from their perspective, you'd be insane not to believe it. Everything had a satisfactory supernatural explanation (or even several competing ones), and there was nothing in their body of knowledge to suggest the vast complexities of modern science which "demystified" (much of) the European worldview. There is so much inexplicable in the pre-modern world, and the creatures of folklore were the best answers to otherwise impossible questions.

Unfortunately, I can't give you a complete, well-rounded answer, but if you want to know what at least one sane adult in 11th century Byzantium believed, here you go (taking satyrs as his example) :

"...God created two rational natures --I speak of angels and men; besides these, we know of no other rational being.The angels remained --and still remain-- in light and holiness...men, honored with reason, lapsed from right thinking, wandering from the truth. Unable to bear our loss, God descended...to save the world...died willingly, was resurrected by his own power, and resurrected us with him...We have found nowhere that he came to the Satyrs as well, or resurrected them; and if the Satyr was a rational being, then tell us: which prophet or apostle or teacher was sent to teach them? For it is obvious, if they were as rational as men, the Lord would have come to them, as with men; show us, then, the Gospel to the Satyrs."

The same logic would apply to other "rational" beings, such as elves, trolls, fairies, etc. presumably.

But he didn't reject fabled creatures completely; they were too prevalent in the Lives of the Saints for a proper Christian to do that, but he could still rationalize:

"...we have heard from the desert saints about dragons and other snakes, the asp and the basilisk, lions and unicorns and other beasts and kinds of animals -- the onager too--that live in the desert"

"The dragon is a kind of animal -- I am not saying dragons do no exist -- but they are snakes, born of other dragons, small when they are young, large and thick when they grow older, exceeding other snakes in size and girth...more than thirty cubits, they say, and as thick as a beam. Dio the Roman...says that when Regulus, the Consul of Rome, was fighting against Carthage, a dragon suddenly crawled into the Roman camp...a hundred and twenty feet long and the same in width. There is also another species of dragon that has a wide head and golden eyes....all the species of snake are venomous, the dragon alone has no venom.." .etc. etc.

The source for the above is the 11th century Strategikon of Kekaumenos. I don't know if there's an English translation. The version I used is this (p.80-83)...but it's in Greek -- the above is my own rough translation.

The Muslims of Andalus and Sicily definitely saw jinn as an accepted fact. Belief that jinn exist is a part of Muslim faith. The Qur'an address them directly at times in fact and is seen as a revelation for both humans and jinn, it even speaks of the conversion of a group of jinn. Malik ibn Anas, the founder of the Maliki school of jurisprudence that dominated in Spain and had a large following in Sicily, had this to say about human-jinn marriages: "It is not against the religion, but I hate to see a woman pregnant from marrying a jinni, and people would ask, 'Who is the husband?' and then corruption would spread among Muslims."

Source: Islam, Arabs, and the Intelligent World of the Jinn by Amira El-Zein

Also, not 100% directly related, but check out this Moroccan piece of (probably black) magic someone recently found in their apartment and posted to /r/Arabs. The names in the squares seem to be jinn lords the caster wish to do his/her will. Many Moroccans are descended from Spanish Muslims expelled from their homeland after the reconquista. It also shows that acceptance of magical creatures as fact has not disappeared.

A number of descriptions given the name dragon, including the one mentioned by growlinghamster and the one here are quite clearly describing large pythons of Africa and Asia. Modern dragons have wings and legs, but the basic text gives a description of a python which is about as accurate as a description of any other real animal in the bestiary, so I'd argue that anyone believing that description of a dragon was believing in a real animal.