It's not as bad west of Twin Peaks, but there are still homeless folks living there. I'm baffled by the folks who think there aren't any homeless people out west (presumably they never go out at night). You'd be hard pressed to find any city in the Bay Area without a homeless problem.
Not really in the western neighborhoods except in a few select spots. You can live in those neighborhoods without seeing it except when you go to the grocery store, parts of Golden Gate park, or the beach
You're joking, right? Personal experiences with the other neighborhoods you've mentioned aside, the Haight has been a mecca for drug use and homeless youth for more than fifty years now.