Why is my dog's fur (down the middle of her back and tail) spotting and falling out?

She may have mange which is treatable. She may also just be getting old.

maybe hot spots, also treatable

allergies or fleas? benadryl may help.

You have not supplied much information, but my first guess would be that she is hypothyroid. Hypothyroid dogs tend to be middle aged to old, often overweight, and have thickened, blackened skin with hair loss and poor coat.

In any case, she needs to go to your vet for a workup. Possibilities include bacterial, fungal, parasitic, nutritional, hormonal, and genetic causes.

the thing is that she’s only nine months old…
it’s not fleas because we’ve treated her for both fleas and ticks, and that’s as far as we’ve come.
what is mange? also, what are hot spots?

Mange is an ectoparasite. There are two types of mange based on which organism is present. A hot spot is an inflamed, weepy wound that is caused through self mutilation.

Again, you need to take her to your vet for an exam. They will be able to investigate and hopefully determine a cause.