Yes. The site is designed so that paper downloads will be counted in RePEc's access statistics.
There are many reasons for this, but the most practical would be for its inclusion in the RePEc archive. All papers that are listed on this website are also part of an archive that we maintain for listing on RePEc.
No, in fact we have many working papers listed on this website! The only requirement is that your work pertains to the discipline of field experiments.
You can make submissions to this website by emailing a pdf copy of your paper to Francesca Pagnotta at fpagnotta@uchicago.edu