Q:

Is there a way to easily manage items when using the Trade Depot? 

When I open the Trade Depot there is a list of thousands of items, not alphabetized.    Is there a way to search through the list without manually scrolling? 

A:

AFAIK, in vanilla DF, there are no search options in the Trade Menu (apart from when you select the items to be brought into trade). 
However, a user by the name of falconne at the bay12games forums has developed a plugin that enables, among other things, searching through the Trade Menu. 
You can see some of it's documentation here (original page) and here (DFHack GitHub page).  It is now included with DFHack r3, so installing it will enable that feature. 
For the Trade Menu, the following applies:
q: Search through the left side list (the trader's list)
w: Search through the right side list (your item's list)
Alt + c: Clears the searches.  This is needed because, while searching, you will not be able to trade. 
While searching, the value and weight values refer only to the items currently selected and in trade. 
A good way to trade several items without resorting to macros is to export everything onto Bins.  This way, you only search for "Bin".  This eases the trouble of selecting each Bin near-individually.