The same note on two staves
I have put red arrows where I am in trouble. As I understand this, I should hit D but it is already pressed down. Do I misunderstand something or it is a typo?
In cases like this you should play the second D, cutting the first one slightly short to accommodate it. It's not a typo, just a choice by the arranger to take the least complicated & most readable approach to notating the music. Think of the printed music as communicating the intended sound, rather than exact movements of your fingers, and it should make more sense.