OS X reinstallation and Amazon software.
I the first place, there are ways of resetting the Administrator's Password. 

Answering your questions, yes, you can reinstall the computer without this password. Just follow Apple's instructions. 

And, yes, you'll be able to re-download the software from Amazon, as stated in its Help Page:


  You can download an unlimited number of times for personal use. To re-download, go to Your Games and Software Library through the "Your Digital Items" link at the top of the screen and click the download button.


And, again, yes, making a clean installation will make a new Administrator user, with a new password which will be chosen by you.

Note: Both of the links regarding OS X reference Lion, as you never stated which version of OS X you are using. These instructions, though, will work for Mountain Lion too.