Simple question about unity 5 rigidbody/gravity

When a object is falling down, the speed increases, is it possible to not increase the speed, so it stays at the same speed?

Gravity is a force like any other including the forces you can add. It increases the velocity over time i.e. causes acceleration so no, gravity won’t just instantly set it to a specific speed.

If you want an object to move in a direction at a constant speed then stop the effects of gravity on it by setting Rigidbody2D.gravityScale to zero and simply set its Rigidbody2D.velocity to a downwards velocity.