Will eczema go away without treatment?

Yes. Most infants and tots will grow out of their eczema. But not all will. And it might take a few years. So you should treat in in the meantime. Start with topicals like vaseline, aquaphor or eucerin. Try diaper ointments. My rule of thumb is that it should come from a tub/jar, not a pump bottle. Then if that isn't enough, then talk to your doctor for a prescription. Keep them from scratching!
Yes. Ecxema generally improves significantly by 3yr. Treatment approaches can be simple with few side effects, like otc creams & ointments. Prescriptions meds may lead to rapid improvement but come with potential side effects. The 1st goal of prescription is to keep the skin layer intact so germs don't get thru. Thickened skin, though yucky, continues to protect the body. Stronger meds can be used when needed.
Yes. The key to treating eczema is moisturizing the skin two to three times a day with a heavy (scooping out of a jar) moisturizer such as eucerin, vaseline or cocoa butter. Only if the skin still develops bumps is a steroid cream usually needed.