Can anybody tell me if a person is allowed promote (advertise) their own software to do with cooking on the site? I can't seem to find that answer.
Essentially, if mentioning a given product will genuinely help answer a question, then you may do so, but you must disclose your affiliation.
However, thinking of this site as a way to advertise is a really, really bad idea. It's a cooking Q&A site, and if you are here to do anything other than constructively answer questions, you're not in the right place, and things may go poorly for you.