Welcome to the forums!
I'm glad you have rescued this budgie and have given her the loving, caring home she deserves.
It's true that older budgies will slow down a bit more with time, but they still have moments throughout where they are active/energetic.
If your budgie had such an abrupt change, then something may be off with her.
Besides the lack of activity, have you noticed a decrease on her appetite, is she sleeping more often? Are her feathers puffed up most of the time?
The gentle nibbling you are describing isn't negative, that's the budgie's way of showing affection, by preening your hand/fingers.
After a budgie reaches adulthood (at 1 year old) it's not possible to give an accurate estimate on age. In your case, you will have to rely on the information given to you that your budgie is at least 5 years old.
Budgies preen on a daily basis, this is part of their hygiene and it's normal for a few feathers to naturally fall off during this process.
Budgies will also moult at least 2 times per year, so it's normal during this time to see an increased number of fallen feathers.
The seasonal moults will usually start in Spring and at Fall, but it's not unusual for budgies to have lighter moults throughout the year.
Please check these links below for the detailed information:
Since you are relatively new to budgies, the information on the several articles and sticky threads located at the top part of each section of the forums will be extremely useful and most (if not all) of your questions will be answered there.