Can small children with asthma eventually be cured?

Maybe. Many children under age 2 wheeze with respiratory infections often treated with asthma medicines for relief - reactive airways disease. If relatively mild outbreaks they often outgrow it. Those who flare up frequently without an infectious trigger are more suspicious for true asthma. Dailey inhaled steroids can help reduce flares and allow the lungs to grow.
No, this is a myth. There is a difference between wheezy episodes in young children & the diagnosis of asthma. Wheezing can occur in children due to viral illnesses (rsv, common cold) prematurity, & environmental tobacco smoke. As the child's lungs grow, the wheeze abates. Asthma can start at any age. Cough is the most common symptom. High risk factors are an allergy diagnosis & family (especially maternal) history.
No, but. Asthma is not a curable condition. It is a treatable condition that may improve with maturation of the immune system and lungs. The real question is, is it really asthma? Since certain illnesses like RSV can cause asthma-like symptoms for up to 6 months, a diagnosis of true asthma requires more than 6 months of symptoms. If a child gets over asthma it probably wasn't asthma to begin with.
Depends, not really. Studies have shown that if a 3 years old, has had 3 or more wheezy episodes in a year, has proven personal allergy and has a parent with a history of asthma, then this child has a 60% chance of having asthma. If all three aren't present then 95% chance it isn't asthma and they will outgrow it. Young lungs with small bronchial tubes are likely to wheeze with viral infections and not have asthma.
Depends. It depends on what is meant by asthma. 2/3 children under six wheeze with upper respiratory infections. Half will outgrow this problem. Risk factors for persistence include eczema, family history of asthma & allergy & cigarette smoking in the home. Several studies strongly suggest that allergy immunotherapy started at an early age & given in appropriate doses can prevent & even reverse asthma.
Rarely. Occasionally, asthma is caused purely by allergic sensitivity. Allergy shots can turn off the production of allergic antibodies and have been shown to product long term remissions or "cures" in both nasal allergy and allergic asthma.
Not Necessarily. Young children with "asthma" or reactive airway disease can potentially improve over time and no longer have as significant respiratory issues but I would not say that asthma can be "cured" nor truly "outgrown". If so, then the original diagnosis should be called into question.
No, but... "cured" suggests a permanent situation. Some children with asthma can lose the asthma symptoms, but always carry with them the genetic predisposition to re-developing the symptoms of asthma at a later time. Studies show that children with asthma fall into 3 categories: 1/3 get better, 1/3 get worse, 1/3 stay the same. Treating the allergies (with shots) in allergic asthma can improve symptoms.
Not yet. Children who develop symptoms in the first three years of life may be more likely to outgrow it than children who develop it later. Current medications do not seem to change a child's chances of outgroing the diease. Risk factors for persistent asthma include: parents with asthma, environmental of food allergies, and tobacco exposure.
Kinda. While asthma is not technically curable, young children tend to "outgrow" their asthma, and might not need long term medication into adult life - not a guarantee, just a possibility.