If I am a legal alien with a 10 year visa and have been married to my husband for nearly 7 years, would I have to leave the US if we got divorced?

If you are a permanent resident, it does not matter that your card is a 10 year card; your status is granted for as long as you live in the US.  IF you divorce, you will retain your status and would not have to go back to your home country.  In fact, once you have been a permanent resident of the US for 5 years, even if you are no longer married to the spouse who had petitioned for your permanent residence, you are eligible to apply for US citizenship.