About Nozomi not being able to wear a ring at work - when I first read the strip, two things immediately came to my mind:
She might be working somewhere with a dress code. Many Japanese businesses/companies have a strict dress code which you are expected to adhere to. I know some more conservative companies don't like their female staff wearing pants and high heels. They are also discouraged from wearing heavy make up or jewelry.
She doesn't want to openly flaunt her relationship with Eli because Japan isn't exactly very open to gay relationships.
also she can be working in a temple, lets remember that nozomi was helping at a temple in the anime
