1) Yes, she needs to be fixed. Unless your dog is actively being show in dog shows or will become a FANTASTIC working dog, you should fix your dog. Millions and millions and millions of dogs are fixed safely every year. It is a very very very safe procedure. Puppies as young as 8 weeks get fixed. Your girl will endure a safe spay.

2) It's probably allergies. Contrary to popular belief, most allergies are NOT nutritional. Most dogs are allergic to dust and pollen and such in the environment. These are the most common allergens, NOT food allergies. To help with enviro-allergies, you'd be best off getting an air filter and placing it near where the dog spends most of its time. It is also beneficial to talk to your vet to see what kind of medications s/he recommends.