If (も) appears after counted nouns, periods and quantities, it's generally used for emphasis. In this case (10年も), it emphasizes the period. Note that in other cases, も after numbers can also mean (more than).
住んでいる indicates a continuous action. First you have the verb 住む, you turn it into its (-te form) --> 住んで and add いる --> 住んでいる. If you haven't learned such a verb form yet, then all you need to know for now is that this is what it means. In our sentence it literally means "has been living".