she tends to hover over our desks until she gets her questions answered not picking up hints to leave. People, including myself, are getting frustrated when we are bombarded with these questions during work.
I'd tell her, "I'm sorry, but I'm trying to work here and you are distracting me with your questions. I can't get my job done properly when you hover around like this." If she persisted, "Look. I have a lot of work to do and we aren't getting paid to chat. Please stop. I don't have time for this and you are stressing me out."
The major problem that I have been having however is regarding her behaviour surrounding our lunch breaks.
Regarding this, could you try telling her the truth? "I'm not trying to hurt your feelings, but honestly, I find your behavior to be very overbearing and needy. I need to use my lunch break to destress and I prefer to take it alone. Please understand that I don't want to eat with you every day. When you ask me every day, sometimes multiple times a day, about my lunch plans, it causes me a great deal of unnecessary stress, because I feel pressured to eat with you, even though I understand that you're just trying to be friendly. Have you tried eating lunch alone? You don't always have to eat lunch with someone. It can be quite a relaxing experience. You should try it out."
The last thing I want to be is insensitive if it really is a disorder she has.
Ok, so I have ADHD and I'm not saying that this should apply to everyone and every disorder, but I strongly believe that if I'm burdening other people, I don't get a free pass by blaming ADHD and that it is my responsibility to find a way to deal with it. For example, even when medicated, I have a hard time hearing and retaining information, so when a coworker gives me instructions, I write down everything so I can refer back to it later.
One of my former coworkers had a terrible memory, but she never wrote anything down. Her solution was to interrupt me and everyone else constantly, asking over and over for months how to do things and then whine when we couldn't drop what we were doing to help her right away. She drove everyone insane, but when we asked her to write things down, she blithely replied that it was a waste of her time to do that, because it was faster to just ask.
In my opinion, telling the truth is not insensitive. For example, I've been told in the past, "I've noticed that you have made x, y, z mistakes. Please fix this problem." This problem may be because I keep forgetting certain steps, but it doesn't matter why, because it is up to me to come up with a way to prevent that issue in the future. It is absolutely my problem if I don't even try to deal with it. Although it might hurt my feelings, being told the truth is helpful, because I may not even have noticed the problem.
Insensitive is being told, "You don't have ADHD. You're just lazy. Everyone forgets things once in a while. You're just over exaggerating your problems." Insensitive is blaming that person's unintentionally problematic behavior stemming from a disorder on malicious intent, i.e. "You didn't forget to do that task. You just didn't feel like doing it, because you're a lazy bitch."
Your coworker is not picking up on everyone's hints and how she's annoying everyone. Maybe if someone spelled things out very clearly to her, even if she has Asperger's or autistic, she could at least try to change her behavior so she isn't bothering everyone. I'm sure therapy would be helpful for her to learn coping skills and how to handle social interactions.