I know I'm not answering your question, but 3. doesn't seem correct to me. I would write "since she started living here/since she moved here". I can't find an example where "since" is used with the present perfect (in the meaning "from the moment, day, year... when). It refers to a precise moment in the past, and the correct tense is the simple past.
That sentence you are referring to is from Longman Contemporary English, Pieanne. I find it hard to understand why we need to say that instead of what you said, too. A native speaker can clarify these for us I think.
All I can say, as a native speaker, is that no.3 (She's made a lot of friends since she's been living here) is commonly heard. I think Pieanne has a point, though, from the grammatical/semantical angle. Since would have to be understood as during the time; I don't kno