I've answered a couple of questions correctly but they are yet to turn green. Am I supposed to notify the moderators or do not. I'm not sure.
As James correctly says in his comment, the person who asks the question is the only person who can select the correct answer. This is particularly a problem with ID questions for which a lot of people join the site to ask one question and don't stay long enough to learn the etiquette of the site.
Your contribution to the site is however very welcome!
For more information on 'accepting answers' you can view the relevant help pages.