What are other causes of leg/feet neuropathy besides diabetes?

Many. There are so very many causes of neuropathy that space here would simply not allow. However, the most common causes besides diabetes would include alcoholism, toxicity (seen in patients who have been exposed to heavy metals or chemotherapeutic agents and radiation), nutritional deficiencies, genetic, compression, certain arthridites and many more. Some are never sourced and are called idiopathic.
Several. Chemotherapy and heavy metal poisoning both can cause neuropathy.
Many. If it has been confirmed that the leg symptoms arw coming from the periphery and not the spine, there are many causes with diabetes being one of the most likely. Drug toxicity, alcoholism, metabolic disorders, infectious diseases, radiation, vitamin deficiency, autoimmune, traumatic, and primary neuro diseases are possible. A neurologist can help figure this out.
Further work up. Multiple things can cause neuropathic pain. I would suggest prompt neurologic work up by a physiatrist or neurologist to include mri, bloodwork, and/or emg. Differential diagnosis for nerve pain in the feet is large including peripheral neuropathy, lumbosacral plexopathy, peripheral nerve entrapment, lumbar stenosis or radiculopathy, or spinal cord or brain disease.