How can Mario jump so high? Is he super human with muscles that can exert more force faster than ours?
The Mushroom world has lesser gravity than Earth so people jumps higher. Also magic plays an important role. Additionally don't forget that Mario and Luigi train every day on perfect jumps. You'll see it in M&L (Mario & Luigi)
Does he have a steel plate in his head and a reinforce spine that allows him to hit his head on so many bricks?
He hits them with his fist. Also his fist is strong.
What about the Super Mushroom, Fire Flower, and Starman?
Those are items and not living people, althought they have eyes. The mushroom people made them that way to give them a nicer look
Note that Mario and co. collected so many extra lives that they are now semi-immortal. That's why nowadays Nintendo is filling up their classic games with lots of extra lives (I never lost all my lives in SMA3) and here's why Mario, Bowser play tennis, kart racing and boardgames instead of trying to destroy each other. It's just not worth it.