A bead on the wire loop
What other forces might be acting on it (other than normal force by the loop and the gravitational force)?
Actually, those are the only forces acting on the bead. However, keep in mind that there will be "inertial effects" coming into play here. For another example of this, think of the example of a bead on a rotating, horizontal, straight wire. In that case the only force acting in the horizontal plane is the normal force that acts perpendicular to the wire, yet the bead will slide outwards with an increasing acceleration.
In your case and in the bead on the horizontal wire, it is much easier to gain intuition looking at the system in a rotating reference frame that rotates with the system. For the horizontal wire case, we then have a centrifugal force that pulls the bead outwards. The same is true in your case. The hoop needs to be rotating fast enough so that the centrifugal force is strong enough to overcome the weight of the bead.
However, as I stated before, in an inertial reference frame the only forces acting on the bead are its weight and the normal force supplied by the hoop. The bead still follows $\mathbf F=m\mathbf a$, but to get an actual expression for the normal force is pretty involved. Nevertheless, this technically is all you would need to describe the behavior of the bead.
The most important of these two is the former, as when I imagined this in my head I cannot think why it should move upward because it looks like it should remain at the lowest point whatsoever be the angular velocity (because if it is like a particle and is at the lowermost point then it would lie on the axis of rotation and hence should have a zero acceleration.)
Your reasoning here is correct if the bead started at the lowest point. Then it will ideally remain there forever (the same is true for the horizontal wire example with the bead starting on the axis of rotation). However, if the hoop is spinning fast enough this point becomes an unstable equilibrium. A slight disturbance will cause it to move away from this point on the hoop (this will happen on its own if you did this in real life). I suppose the problem could have been more precise by stating the additional assumption that the bead is not starting at the lowest point on the hoop.