Astro File Manager does allow you to create folders, rename files, and move files from folder to folder...has a photo viewer but is not great. It is a great tool for managing files on your phone and has many options. It's not ideal for pics, since it is cluttered with many other files and options, but it will do what you need it to do...and it's free.
However for organizing 2,700 pics I think connecting to PC and doing it over USB connection would be easier to get you started. Mount your card then move your pics/folders in bulk....seems easier to me.