I'm gonna jump on the blood panel side as well. a CBC/SAP (Complete blood Count/Sick Animal Profile) wouldn't be a bad thing, get everything checked and then you will know if there is any medical reason for the weight loss and skin problems.
Also, since she is having trouble shedding, get a good brush and brush her every week or two if she will tolerate it, since the last thing you want is matting of the fur which gets quite painful (especially if your cat is long-haired) make sure to check on her belly and in behind her elbows and groin area since those aren't easily seen unless you look.
Has she had a dental checkup lately? If not then it is well worth getting one, there's always a chance that she could be eating slowly and not finishing meals because it hurts or is difficult due to some issue, much like our horses.
Ask the vets about a food, if you can afford it then a dry food from the vets will be your best bet. I'm not sure what you can get where you are, but I know Hills is a popular brand of very good food in many countries including NZ, they make special diets for the older cats, ensuring that everything is highly digestible so the body system doesn't have to work so hard to get the nutrients it needs from the food.
-Vet food also *tends* to work out cheaper in the long run than supermarket/middle class food, because you have to feed less to achieve the nutritional requirements.
I see you are switching her foods too, I hope that works well for you, if she suddenly decides that she doesn't like this new food, then you can go back to the old one and just put a little bit of water over the biscuits and make them a bit softer
R.I.P ~ Bubbles - 25yo tb mare - 13.04.2011 ~ 8:30am ~ passed away naturally and peacefully in my arms