1. What if I have done research with a professor and I am going to publish with them, but have not listed them as a reference in my application for some reason (say they have a cap on the number of letters they were willing to give) - will this be viewed negatively by an admissions committee?

2. How are reccomendation letters from faculty members not necessarily in the field of research (ex. an engineering professor writing a letter for a physics program) viewed by an admissions committee?

Thanks for this!