Hi Sea,
It sounds to me like your sister needs to spend as much time focusing on her own life as she does on yours! Several points here:
1 You're an adult, not a naive twelve year old. Renting property is a good way of making extra money. it would be madness to have that untapped rental potential sitting there doing nothing. Sometimes you have good tenants, sometimes bad. That's the nature of any business - plumbers get clients that don't pay, shop owners have people stealing from them. My current landlord wasn't going to rent again after his last tenants because they left the place in such a state that it ended up costing him more than he'd got from them in rent.
2 You have to spend half a day eating well and exercising. According to which law, exactly? As long as your life is within the boundaries of the law, what you do is your business and no-one elses. You are looking after yourself and working hard at getting well again. It takes time, effort and patience. Even if you weren't, she has no business telling you you must. This isn't concern, it's control. It sounds to me like she has no control in her own life (tied by the evil aunt because of the house) so she tries to control others. Sad, but her issue, not yours.
3 If people are worried about other people there are healthy, constructive ways of trying to butt in (to put it politely). For example, if she felt you were not eating right or getting enough exercise she could suggest a healthy day together once a week - a walk, a swim, a healthy picnic somewhere pretty. If you wanted to go and found being with someone helpful then great, if you said no thanks then it would be right for her to respect that and not give out to you about it. Similarly, she could offer to vet clients for you, do credit checks, get references etc. Berating you and telling you that you're doing it all wrong is abusive and doesn't help anybody (especially when it sounds like you are doing it all right in the first place!).
I wonder if she sees you getting healthy as a threat? You have a way of making money without having to go to work (via the rentals), you've taken time out to get yourself well and are making progress. Sometimes I think people see you are changing and on some level they know the status quo is going to change, so they try and derail you. I was diagnosed with bi-polar six years ago. I decided to manage it through diet, exercise, therapy and complementary treatments because I found the meds very difficult to live with. There was a lot of resistance to this, with a lot of raised eyebrows about me 'having' to do yoga every day and needing 'me' time. I've been off meds for five years and haven't had any problems. I also have no contact with my family.
I think it's very tough to have to deal with this. You could try a polite "thanks for your concern but I don't want to discuss this" approach. You could be more direct and tell her it's none of her business and to keep her nose out. You could try and avoid her for a while - it all depends on what you think you can cope with. I remember lying to my family and telling them that I'd got a full time job because it was the only way to keep them away. Seems crazy now looking back, but the thought of just saying "Sorry, I'm busy on Tuesday" was just to much to cope with.
Be reassured that it's her with the problem, not you! Keep at it, Sea xx