I don't know if it was native or air browser but I unzipped a few albums I downloaded directly on device... What formats you trying or is it more That You need a zip/rar app....
I don't understand the question. You don't download and install apps other than through App world, or you can download apps to your PC and then sideload them using DDPB Installer on your PC to install the app. Are you talking about either of these methods.
Files & Folders lets you manage zip files as if they were just folders. Copy and paste files into and out of them, rename/delete files inside, view previews & thumbnails, zip/unzip whole folders.
I believe the OP is looking for a program that will un zip a file on the PB. I know I have downloaded zip files that I could not open. I had to transfer them to my PC, un zip them and transfer back.
F&F can unzip most .zip files, directly on the playbook. The only zips that may not work are zips that are "protected" with a password or zips that use a non-standard compression algorithm.