Would the centripetal force still provided by the weight of the mass? Why or why not?
When you spin it vertically, you would most probably spin it with a constant angular velocity (try it out), which means that that the centripetal acceleration required at any point will be the same. However, in this case, the radial component of force due to gravity keeps on changing which means the tension will keep changing so as their resultant is equal to the centripetal force. So that means the slotted mass will oscillate. Also, we are assuming ideality in the sense that the tension is uniform throughout the string, which is definitely not the case.
What impacts does the straight line in the hollow tube have on the centripetal force if it was spun in vertical circular motion?
The centripetal force only depends on the angular velocity and has nothing to do with the length of that tube. If you keep all the other parameters (radius of the circular motion, angular velocity and the mass of the slotted weight) the same, then the only difference due to changing the length of the tube will be that, you will have to apply a larger torque (see the figure below) to keep the tube in its position. This because although the centripetal force is the same, stil the length of the moment arm has increased which means a higher torque.