Would there be Coriolis Effect on a cylindrical planet with no tilt that orbits a star just like Earth does?

Answer 1

No
Coriolis force is basically kinematic due to motion in a rotating coordinate system. It might better be called Coriolis "effect".
One way to look at it is imagine you are a hurricane off Cape Cod sucking air up from the equator. As the air moves north from the equator toward the core, it is still moving east at the same speed as a point on the equator due to the earth spin angular velocity times the earth radius from the axis of rotation. However as it moves north it keeps that big east velocity even as the surface moves slower due to being closer to the axis of rotation. That means that north moving air ends up east of the hurricane core. Air coming from the North of course ends up west of the core. That is a counterclockwise rotation of air around the core.
If the planet were a cylinder, there would be no such effect because the radius would not change as you moved north or south from the equator..