Oh my goodness Hair. That woman is many levels of bizzare and scary. If she knocks on your door, just pretend that you aren't there. The dog seems like a nice dog. You should keep it if no one claims it. Did it have a collar or anything?
Luckily my driveway is gated and padlocked, so if she comes, I'll meet her out there. No one can just end up at the door un-noticed :~D