Hi Padma,
Quite a lot of questions so I hope I can answer them all.
First off, the way you're using the word "illness" needs a little thinking about. Your MC might experience either depression, anxiety or post traumatic stress disorder from the abuse and while these are "illnesses" of sorts they're also more than that.
The main thing for children who've found themselves in care are issues of confidence and self esteem. They may also have an attachment disorder if they come from very unstable homes. To try to explain this, common wisdom recognises that children have a couple of very close and important relationships, usually with Mum and Dad. It's easier to explore the world and take risks when you have a solid relationship to go back to.....to conjure up an image think of a toddler running back to Mum when a stranger in the same room does something to unsettle them and hiding behind her peering out. Now imagine how exploring the world would be different if you didn't have one safe and solid person to run to when you were upset. In two different types of attachment disorder children might either treat everyone with too much familiarity even though the relationships may be superficial, or they find it hard to trust anyone. This isn't an illness. It's just something that can happen to people when they don't have the things we take for granted and it can effect future relationships.
It would be a good idea to research a bit about psychotherapy and cognitive behavioural therapy too as treatments. Depression, anxiety and PTSD can respond to a loving home and loving family, and they might also improve with hypnotherapy, but attachment disorder is very different. Not many people would identify with your plan to cure your MCs ills with hypnosis, unfortunately life isn't that simple and the way that young people from difficult backgrounds find something better is by a lot of hard work and determination on their part, and usually by finding the stable relationship they've missed out on. That can be with a partner, not just with foster parents, but it takes time. If a family spend a few years messing a young person up they'll need a long time to work through it. You might sell your MC short by making the "treatment" for their "illness" too simple.
As for where they end up, if they're under 16 and have nowhere to go then a social worker will have to find them somewhere. This might be with a relative, or it might be in a children's home. From there everyone would do their best to provide a foster family but demand is greater then supply.
A third point is that "adopted" and "fostered" mean different things. An adopted child is placed with one family by a court who adopt them forever (at least that's the plan although that sometimes breaks too). Someone in foster homes is not an "adopted" child. They're a looked after child who is being fostered in a place found by social workers. It's a small point but an adopted child would not be in a foster home, they'd be with their adopted family.
There are different ways to become looked after too. The local authority might have a care order giving them parental responsibility for the young person and this usually means the young person has been taken from their family. Alternatively they might have been put in care by their family in which case there would probably be no care order and family would still be involved in some way. If a child had lost their parents then they will have temporarily been a ward of court and then a care order given to social services.
If your MC has biological sisters then social services will do their very best to keep them together or to keep them in contact if they can't.
Not surprisingly, how you get into care plays a big part in how it effects you. Being kicked out by abusive parents is a very different experience from losing your parents in an accident, and being taken from your family by a social worker is different again.
Craig