Why the rotors spin in opposite directions
Every spinning rotor pushes back on the body with an equal and opposite twist. If all four spun the same way, the drone would spin like a top. Pairing two clockwise rotors with two counterclockwise rotors cancels that twist when they run at the same speed, and gives the flight controller a way to turn on purpose by unbalancing them.
Thrust is a vector
Tilting the whole airframe is how a quadcopter moves sideways. The rotors still push along their own axis, so a tilted drone splits its thrust into a part that holds it up and a part that pushes it across the field. That is why a drone needs a little more throttle to hold altitude while it flies fast.