I've kinda turned away from my Science Fiction Robot idea, because I felt too much of the idea was already done, and kinda heading toward the "Magical Beings Live Among Us" story. But I wanted to steer off the normal path of magical beings hiding in plain sigh -- instead, the idea is that magical beings have lived among humankind since the dawn of sentience on Earth. There's no big, secret reveal by the government or trying to keep them [magical beings] secret: they've always been there. Actual events in history would have appropriate twists. One example would be that the Holocaust was to eliminate magical beings from Germany instead of the Jews. I want there to be magic BUT there is also scientific explanations on numerous things in this alternate world. Magic would be a certain gene that could or could not pop up in your children, it'd be pretty random at times. A father who has magic in his genes might not have magic capability but his son could. Mages would be carefully observed due to the fact they can warp our [us, in reality] laws of physics. Magical Beings would be based off the actual myths and legends -- genies would live in the Middle East while Centaurs would be found in the Mediterranean, etc. For some topics regarding this kinda universe, could there be scientific explanations you guys can provide for things that'd usually is explained by 'magic'? How would Eastern Dragons fly without wings, how could dragons breathe fire, how could shapeshifters work, etc.
I think you're onto a tricky one here, however I will try to help. Going on the principle that anything sufficiently advanced appears impossible I would suggest looking at where the 'edges' of science have got us so far. I suspect that the proposed existence of the graviton (gravity's force-carrier particle) could be relevant to things that shouldn't fly but do, scientists so far have not been able to prove it's existence other than by inference so it could be good. I would certainly advise reading up about it a bit first. Dragons breathing fire is normally explained by them having some sort of gas bladder where they store something flammable. They could potentially light it with some sort of electric current or with something that makes a spark, like steel on flint or some similar reaction. Looking back at this sentence I wonder about the "normally explained" - I've certainly read a few books that purport a similar theory, but I do not remember the names of any of them at all. Shapeshifting could be control of your body on a cellular level. If this were the case you would only be able to shift into objects/creatures of equivalent size. Shapeshifters would at all times need lungs/heart/liver/kidneys etc - I don't think that you can reasonably reconcile the concept with science otherwise. Also it would hurt. A lot. Genies and djinn and all that sort of thing would be difficult I think as they are incorporeal and that's always going to be tricky to explain. You could give them a proper, physical body but then what would their powers be? For an easy-to-understand guide to quantum physics/force carrier particles/how things are stuck together I would definitely advise going to particleadventure.org - depends how much you already know though, don't want to patronise.
You are going to find that science is on par with magic in these cases. Have you ever seen Smallville, the TV adaptation of Superman? It's kind of awesome, but the main problem in the first few seasons is the "meteor freaks". People infected with Kryptonite who manifest different abilities. The main logical fallacy, of course, is that it effects them all in different ways. Add to this the later addition of Aquaman who was born on Earth in Atlantis and that somehow means he has superhuman strength, the addition of Zatanna who can do magic just because, clones of Lex Luthor who have all of his memories or develop different skills, people who can move faster than the speed of sound or teleport without being destroyed in the process... If you use science, you won't be explaining it. You'll be handwaving it. So settle down with the cookpot of creation. Think about what's logical for your alternate world and roll with it. The moment you start adding absolutely everything to your world is the moment your world starts having no substance.