I feel cautious about this friendship... any advice?

it definitely sounds like you are the one who has the level head in this ongoing situation. the girl/woman you're talking about sounds like she hasn't grown up in a few ways that rear their ugly head frequently. it sounds like these weird tendencies she has are scratching at the surface of deeply burried issues or childhood traumas that she hasn't gotten over. OR- she could just be plain off her rocker. may have one or more personality disorders like Bi-Polar or Mania.