Here are some tips for you:

(1) How to find popular iphone 5 cases in zazzle marketplace?

Just type "iphone 5 case" in search bar and hit the search button. [see the result]

(2) How to pull all products of the category "cute animal" I created in my zazzle store?

Take my store "pencilplus" for example, the url of my cute animal category is http://www.zazzle.com/pencilplus/gifts?cg=196855913760186620
[see the result]

(3) How to find my T-shirts in my zazzle store?

Take my store "pencilplus" for example.
[see the result]