Why does the Hadley cell descend at 30 degrees? George Hadley's initial model of the Hadley cell described air as being heated at the equator, ascending, and then moving aloft pole-wards where it would cool and descend.  Meanwhile surface air would move towards the equator to take the place of the rising hot air there, forming a giant Hadley cell, as in the picture below:



However the modern conception of the Hadley cell is one where air ascends at the equator while air at an angle of 30° latitude descends, with winds moving towards the equator on the surface, and with winds moving towards the poles aloft to complete the cell.  The modern conception of the Polar cell also works in the same manner, with the difference being that the expanding air hot air in this cell originates from 60° latitude, rather than from the equator.



Why is it that the air in the Hadley cell descends at 30° latitude, as opposed to continuing all the way to the poles as Hadley had initially suggested, and why does air then rise again at 60° latitude forming the Polar cell?
The Hadley cell was proposed and works only for a non-rotating earth. When we consider the earth's spin, we have to consider the Coriolis force as well. Because of this force air cannot travel in one unhindered cell from the equator to pole or back. So there must be an odd number of cells together so that the air rising and falling in the adjacent cells is oriented in the proper direction. Considering the various observations of the Easterly and Westerly trade winds a 3 cell model best explains our atmospheric circulation. The location of the majority of earth's driest and arid regions are located in the areas underneath the descending branches of the Hadley circulation around 30 degrees latitude, which also supports the 3 cell model. 

Also watch this video which gives a great explanation to all of your questions with the help of practical experiment and animations.
Atmospheric Circulation Video