It sounds like you have done what you can for Eve to make her happy in your relationship. The fact that she left after hearing from her doctor that she has to think about who would take care of her may mean that she feels under a lot of pressure to put the responsibility on someone. She may not have wanted to put it on you. She could have trust issues or feel that making you responsible for her was too much and not fair to you. It depends on how she acts about it as to what reason it is. You mentioned that she is parking outside of your company and watching people. That shows that she feels upset and bothered by something, maybe her decision. She may want to be involved with your life and can't bring herself to come back yet. So she stays "in touch" with you by being around parts of your life that are important to you. Or it could be that she is not sure how to handle the issues in your relationship and with her eyesight, so she is hanging around your company as a way to deal with her feelings.
Eve may very well lack relationship skills and may not be able to express how she feels about the stress
she is under. But without more details than that, it will be hard for you to say how she will be in your relationship. Being told that your eyesight is going to be gone in so many months is a terrifying thing to hear. And the amount of stress Eve is under has to be enormous. She may not be able to react in a normal way in your relationship because of the amount of stress. She may take out her feelings on you or even herself in dysfunctional ways in an attempt to cope. That does not necessarily mean she is not able to be in a relationship, it just means she is under a lot of stress.
The best way to react to her is to be steady and reliable. Be there for her but also allow her some space to work this out on her own. As long as she doesn't cross boundaries with you (such as starting to stalk your employees or you), it is fine to allow her some leeway in how she responds to you or acts with you. Try to let her decide when she feels comfortable being with you and allow her to set the time when you both get back together. Be as supportive as you can. And remember, you have your own needs too so if it gets too much, don't forget to take care of yourself.
I just got your additional question. It sounds like Eve might be involving herself a bit too much in your family situation. It is not her place to be informing your sister about anything related to your mother's estate. Although this might just be a mistake on her part, you may want to talk with her and set some boundaries. Until you and Eve are married, she needs to let you handle these types of situations. And in the future, she needs to talk with you first before she discusses any issues with anyone in your family. As long as you let her know in a firm yet gentle way, it is perfectly fine to tell Eve how you feel.