Burning. Burning hands and feet can be associated with diabetes and it also is associated with alcoholism and other conditions that produce neuropathy. If you know that you have diabetes and you also have burning hands and feet you can receive prescription medication that can help. Consult a podiatrist or neurologist.
Depends. Are you diabetic? For how long? Peripheral neuropathy is definitely associated with diabetes but also has other causes and should have a full work up and not assed it is diabetes right away just because you have it, even if for a while. That would not be fair to you.
Possible neuropathy. Neuropathy can happen as a result of trauma, or nerve damage due to the consumption of alcohol or certain medications. Symptoms can range from a numbness and tingling sensation, possibly a burning sensation, to an uncomfortable painful sensation of the extremities. Get evaluated by a professional to determine the exact cause in order to get the appropriate treatment.
Yes. Yes it could be. It could also be associated with leprosy, syphilis, spinal lesions/injury, idiopathic (no apparent reason) neuropathy, etc. Any more details?