Stepparent Adoption in Nevada

I am hoping for some advice on a step-parent adoption in Las Vegas, NV. My son turned 5 in December and has never met his birth father. I was 17 when he was born. I have never received a child support payment, and he was not even on the birth certificate. I had a child support case open due to my son receiving Medicaid and their requirement to keep an open case. Last month I was called in for genetic testing because my son's birth father was either found or came in to respond (they wouldn't tell me specifics.) He has called me about 5 times total in the last 5 years, and just a few days ago began messaging me on a social network site asking to see his son. I have been in a committed relationship for 3 years now, and we have a 7 month old little girl together. We live together, but are not married. My son calls him dad and he acts as his father. My son has no knowledge of his birth father, and as far as he is concerned my partner is his father. We have always planned on pursuing a stepparent adoption, but the urgency was never there due to my son's birth father being completely absent in his life. Now, with the current developments it has moved to the top of my list of priorities, however, I don't even know where to start. First, is my partner eligible to adopt my son even though we are not married? If not, is the a requirement that we have to be married for a certain number of years before it can take place? If need be, we'll go get married tomorrow. Also, is the fact that my son's birth father has been completely absent both emotionally and financially grounds to terminate his parental rights? (He was apparently added to the birth certificate due to the results of the genetic testing.) I could really use some help right now. My son is well adjusted, happy, and doesn't want for anything. I don't want him to have to go through this. He has a father, and I'm afraid he is too young to fully understand the situation. Thanks in advance!