For searching the GTN don't put in your name (or your companions name) in the search fields. That seems to cause more problems. I've been in the game since launch and I can't get that to work properly either.
To give an example, lets say I want a new heavy armor headpiece. My level is 33 and my current piece is level 29.
What I would do in the search fields is select heavy armor, headpiece, * prototype quality (blue) but use premium (green) if you want to as well, level range 29-33 and search. Then it will only show me all headpieces of blue quality and up from levels 29-33. You will also get listings for heavy armors that you won't want because they'll have the wrong main stat on them but I find this the easiest way to navigate the GTN. That may be where the 'search for items I can use' option is supposed to work but every time I try it I get blanks as well, so I don't bother.
*When you search an item quality it will show you all items from the quality you picked and higher, no lower.
Awesome! This helps to clarify a little further. Much appreciated.