Can a child’s ear infection clear up on its own?

It depends. Children <6 months old should always receive antibiotic treatment for ear infections. Children from 6 months - 2 years who have an uncertain diagnosis of ear infection and a mild illness do not need antibiotics. Children 2 years and older do not need antibiotics if their illness is mild or if the diagnosis is uncertain. All children with ear infections should follow up closely with their doctor.
Yes. Yes, indeed many ear infections do get better on their own. But if fever, pain, loss of appetite, or excessive sleepiness persists for more than a day you should see a physician.
Yes. Most definitely they can. Antibiotics, if used, may only shorten the symptoms by a day. If your child is prone to recurrent infections, however, it would be in their best interest to seek the care of a doctor for alternative treatment options.
Yes. Most childhood ear infections get better with very minimal treatment. Tylenol (acetaminophen) or paracetamol or Ibuprofen can be used to keep fever controlled. Warm and cool compresses help pain relief. Don't put drops in the ear if you can't see the eardrum, and never use an ear candle.