Hi, dont't worry. Things will sort out when your baby's older. It's very normal that you are worried for a first-time mom. I think we all are
If you have any worries, just try to get as much information and advise as possible. As your baby is very young, I believe the best person you should request for advise is the pediatrician.
My 2 kids had cradle cap (that's very common). I put natural baby massage oil on it and then comb the hair before giving bath. The cradle cap goes away like that.
You say the head is balding. Does it mean she's loosing her hair? If yes, that's normal as well. Baby's hair will fall after a few months and new hair will grow. If your baby always puts her head in the same position when she sleeps, chances are high that in that part of the head, there's no hair. So that's normal as well. You can change her position every other night.
For the eczema part, have you tried goat milk? She may have allergy to cow's milk that are found in most formula milk. Otherwise, you may try to put baby lotion. I use this excellent Swiss brand: Weleda Baby Calendula lotion. One of the ingredient of the lotion is calendula flower. It is a natural anti-inflammatory and has healing properties. It's recommanded for eczema. There is also a face cream. I used these 2 products for my babies. My daughter had eczema, but only a little bit on the shoulder and face. And it's gone after a couple of days of use. I use also the Weleda Baby Calendula nappy cream which I highly recommend. You can try to put the nappy cream on very dry areas of the body. I did it for my daughter's eczema when it was really dry and becoming hard!
What kind of bodywash do you use for your baby? Most commercial bodywashes has chemicals inside and they can worsen your baby's eczema. You may change to a natural bodywash that doesn't irritate sensitive skin.
For the constipation, it can be caused by the formula milk. Goat milk is maybe better for her. Give her some water between the milk feed as well. It won't cut down on her milk intake. I started to give water to my 3 kids when they were about 3 months old, so I think it won't harm her at 2 months. Ask your pediatrician for advise as I dont't know what other thing you can give her for her age.
Hope it helps and your baby's going to be better very soon. Good luck!