You can use glaxal base cream, which will help to reduce eczema. The root cause of eczema, it is typically related to the food your baby eat, or the food you eat if you are breast feeding. Try to avoid nuts, orange, and avoid touching chemicals. Also wear 100% cotton cloth for your baby and use skin sensitive laundry detergent. Has been a long time and cannot remember all food type details now. Just google around and you should be able to find more information.
头皮总有一层白头屑 can be a light version of another common baby disease, cradle cap. The worse one can develop a yellow layer of hard cap on baby's scalp. Use warm water to wash baby's head, then use very fine comb or soft tooth brush will certainly help. Bath is a perfect time for this. You should also use baby shampoo once a while to wash baby's hair.
Both are very common problems among babies, and no need to worry about.