Can a pinched nerve cause burning and numbness in feet?

Pinches nerve. Pinched back (lumbosacral) nerve roots can cause tingling in sole of foot if around s1 or back of foot if l5... But if both sides, symmetric, more likely a sensory neuropathy.
?tarsal tunnel syndr. Not uncommon to have a nerve pinching over the medial ankle, at the flexor retinaculum, which produces tarsal tunnel syndrome with worsening symptoms on standing and/or walking. However, your problems could represent a progressive peripheral neuropathy due to numerous causes. Get this evaluated and treated.
Pinched nerves. Nerves carry signals from the feet to the brain and from the brain to feet. If the nerve is pinched (injured or inflamed), then it will cause altered conductin and interpretation along this nerve. This translates into pain or burning and/or numbness. Weakness can also occur.
Yes. Nerve entrapment is known for numbness and burning type pain. Get nerve conduction test and either a block can be performed or medication to give relief.
Yes. Definately.