Over 50 years I've run into more than my share of oddballs. I swear they smell the INFJs and attack. This lady is up to something.
She may be living out a fantasy friendship in her head, thinking you all are much closer than in reality. You mentioned she's not present in the moment when you're with her.
I'm not saying zap her from your life, but I would just because these type are so hard to maintain a relationship based in reality with. They drain one person and move on to the next. I'm also biased against anyone who assumes they're owed gifts, money and friendship. Sorry, nope. It takes a ton of work and dedication from both of us for a person to level up to that with me. Probably why I also have only a few friends.