I think the schools chosen by you are right for the score. I think your SoP is in the right direction. To answer your questions:
1. I went to a public admin program after 5 years of exp and considered the same question. Found only Harvard and Duke ( to some extent) having a good 1 year program. Unless finances are an issue, I would advise going for the full course. SIPA has something called advanced standing where you can get a semester waived.
2. This one is tricky, I am assuming you worked with her in some capacity and she basis on the impressions of that. Institutes do often ask for ways to verify that the person writing LoR is bonafide or not. It is always advisable to share the official email IDs for that reason. in your case I would recommend looking for an alternate option. In case that doesn't work, she must mention that she is no longer in the organization ( basically give necessary disclaimers).