The living quarters that are given to the adventurer in the College of Winterhold, are the storage containers secure if one leaves items in them? Do the various items respawn in the living quarters or in the College in general? I looked for this information but I could not find it on the Skyrim Wikia page.

All of the cupboards, end tables and dressers are safe, unless you have a mod like Clothing and Clutter Zguxes that's makes them respawn. Here is a list of safe containers in Skyrim. http://www.uesp.net/wiki/Skyrim:Containers#Safe_Containers