No, they don’t lose fur just because they are getting older. There will be a reason for her hair loss so she needs to see a vet to find out what it is.
How much weight has she lost?
As she is losing weight then she is not eating properly - weight loss means they are not eating as much hay as they should be. Hay is 80% of the daily food intake and you cannot tell they are eating enough by watching them hence the importance of weight checks.
Please step in and support feed her (with either mushed pellets or a proper recovery feed) to stop the weight loss. You will need to weigh her daily so you can monitor that she is getting enough syringe feed to stop the weight loss. Please also see a vet about the weight loss
All About Syringe Feeding and Medicating Guinea Pigs with Videos and Pictures