I think I already know the answer to this question, but to be sure: is there any way to hide item metadata fields that are empty if I'm only running a hosted (omeka.net) site? Also, is it possible to imbed an image in the HTML of a "simple page" on a hosted site?
You can hide empty metadata fields: there's a checkbox called "Show Empty Elements" in the Settings panel that you can uncheck (this only affects the public site).
I believe it's not possible to embed an image in an omeka.net-hosted simple page. An exhibit could work for you, if the image you're attempting to include is part of your archive.