As per the dragons, I agree with Xant, but they possibly will explain it with something like Drogon being the alpha and the others following its lead. Since Dany controls Drogon then the others follow her too.
But they don't explain how she controls
Drogon. They show her teaching Drogon to breathe fire on command. That's like teaching a dog to "sit." Then they show Drogon going absolutely out of control and doing nothing Daenerys wants him to do. Then they show Daenerys having perfect mind control over Drogon, having him go precisely where she wants him to, do precisely what she wants him, etc., etc. It's like if you had a puppy Doberman, you teach it how to sit, then it goes fucking crazy, and next time you see it is when it's an adult and suddenly it's reciting Shakespeare and doing your dishes for you just because you make eye contact.
And the thing is, they made a really big deal out of the dragons being out of control, and not controllable. There were a whole bunch of scenes about how it'd be possible/impossible to train them.
And then they just go "fuck it, Daenerys is magical."