On stellar aberration in the context of ether drag hypothesis In Resnick's book on introduction to special relativity he mentions two effects that contradict the ether drag hypothesis. Fizeau convection coefficient and stellar aberration. He says that if ether was to be moving along with the earth then the light coming from a star directly 'overhead' wouldn't appear to move or in other words we would not have to correct the telescope angle due to earth's motion around the sun. In his words: 

ether is not dragged around with the earth. If it were, the ether would be at rest with respect to the earth, the telescope would not have to be tilted and there would be no aberration at all.

This wiki animation shows what he means. What I'm doubtful about is that since the earth is changing its position with respect to the sun all stars should appear to move in the night sky regardless of the presence of an ether medium. So how does it make sense to argue using this point? Does stellar aberration tell us that no star should be visible directly overhead due to earth's constant motion? Does the star appear to move during the time you're seeing it through the telescope? 
Note: I have studied Michelson-Morley experiment and am quite convinced that ether is an unnecessary hypothesis. I'm only seeking a clarification on the phenomenon of stellar aberration.  
 A: 
Since the earth is changing its position with respect to the sun all stars should appear to move in the night sky regardless of the presence of an ether medium. So how does it make sense to argue using this point?

Stellar aberration is a result of the changing motion of the the earth rather than its changing position.  The changing position of the the earth does result in apparent change in position of the stars due to parallax.  This is what Bradley was looking for when he observed aberration though the parallax effect was smaller than aberration and too small for him to see.  This parallax does not affect "all stars" equally; close stars appear to move more than distant ones.  
Consider also that if some how the earth were changing position at a constant rate (straight line motion) there would still be some tiny motion of stars due to parallax but not due to aberration.  Aberration would shift the apparent positions of the stars but this shift wouldn't change over time.

Does stellar aberration tell us that no star should be visible directly overhead due to earth's constant motion?

No.  Think of the animation you linked to in your question; if the telescope was pointed straight up and moving to the right light from a star would be able to make it down to the bottom of the tube if the star were located somewhere up and to the left, slightly behind the telescope.  In that way the light would have a forward component of its motion that matches the forward motion of the telescope.

Does the star appear to move during the time you're seeing it through the telescope?

Here I'm not sure what you mean.  Stellar aberration amounts to about 40 seconds of arc over six months.  How long are you thinking of looking through the telescope?
A: James Bradley's observations were made using sidereal time, not solar or mean time. This means that over the course of the year, Bradley had to view the star against an ever-changing sky that would go from morning to night and back to morning again. Look up sidereal time if you haven't. And you can read Bradley's work on Archive.org. James Bradley claimed to be able to see the star Gamma Draconis during the day with his 18th-century telescope. We have to assume that he and his followers didn't resort to fudging the observations. We have to assume that seeing a star during the day (even at noon) was not only possible, but that the star's position was not altered by the bright blue sky.
His explanation is not the only logical explanation. And the amount of stellar aberration he "discovered" is a lot smaller and less impressive than most people know. Just look up the definition for arc-second, 20 arc-seconds is nothing.
Bradley's explanation, resorting to rain, has nothing to do with how light demonstrably propagates. His illogically-premised explanation, comparing light to rain, doesn't hold water when one imagines a shower-head as the source of the water drops. Even if one is moving relative to the shower-head, the head is still in the same spot, the shower-head's position does not shift. The shower-head is the star. The angle the raindrops appear to have is an illusion based on motion and doesn't change the position of the source of the water drops. The drops still fall straight down. The angle is the result of the straight vertical rain-drop motion combined with our relative horizontal motion.  Anyone with even a minimum of experience using an animation program like Adobe After Effects can illustrate this.
Bradley's mathematical equations also produce the full 20 arc-second result. The equations do not indicate a rate of change that lead to that maximum north or south value.
