Your child appears to have a very blocked nose. At his age this is usually due to enlarged adenoids. His bad breath comes from his persistent mouth breathing. Please ask an ENT specialist to see him. He will probably need to have his adenoids removed which is a very minor operation these days.
As for his hair cutting performance. He probably had a traumatic experience when his hair was first cut. Try and find a hairdresser or barber who is known to be very good with children. Be very patient with your son and with time things will improve. Will he let you cut his hair? This may be the best solution.
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