Scared Cat and Bad Fur, First time cat owner

I just got married and my wife's cat has a lot of problems and I want to find some way to help it. She got it at a shelter. It is afraid of almost everything. After her owning the cat for 8 years, the cat is still afraid even though my wife if very loving to it. It is affectionate with us when we are lying down.
2. It has fur that always looks like somebody that hasn't washed their hair in a week, even though my wife brushes her nearly every day.
3. She hacks and coughs up hairballs all the time and sometimes gets allergies.
4. She eats only small amounts of food.
5. She isn't playful or curious about things.
What can we do about the being afraid and coat problems? Any other advice would be appreciated too.
Thanks, Wholelottabubba

Some cats are just naturally skittish, I've had Crystal for 11 yrs now and she was from a pet store and has just recently started to relax around people.
You may want to try something like Feliway, I haven't tried but have heard many good things about it.

Her fur problem could be from different things. Has she had a check up from the vet to rule out any illnesses? It could also be from the food she's been eating. What brand is she eating presently?