Hello XXXXXXX
Thanks for your query.
Congratulations on having your baby at home !

A premature or preterm baby is born before 37 weeks of pregnancy have been completed. Generally, the earlier a baby is born, the higher the risk of complications.

At first, your premature baby might have little body fat and need help maintaining body heat. He or she might cry only softly and have trouble breathing. Feeding your preemie might be a challenge. Yellowing of the skin and eyes (jaundice), low blood sugar, and lack of red blood cells to carry oxygen to your baby's tissues (anemia) are possible. More-serious concerns might include infection, episodes of stopped breathing (apnea) and bleeding into the brain. Some preemies have impaired hearing or vision. Others experience developmental delays, learning disabilities, motor deficits, or behavioral, psychological or chronic health problems. Many, however, catch up and experience normal healthy development.

The first challenge is to establish your milk supply. Breast milk contains proteins that help fight infection and promote growth. Although your preemie might not be able to feed from your breast or a bottle at first, breast milk can be given in other ways — or frozen for later use. Begin pumping as soon after birth as possible. Aim to pump at least six to eight times a day, round-the-clock. Also, ask your baby's doctor about your baby's need for supplementation — either in the form of breast milk fortifiers or preterm infant formula.

Spend time with your baby. Speak to your baby in loving tones and touch him or her often. Reading to your baby also can help you feel closer to him or her. When your baby is ready, cradle him or her in your arms. Hold your baby under your robe or shirt to allow skin-to-skin contact. Learn to feed, change and soothe your preemie. . Consider personalizing your baby's bed with a special blanket or family pictures.

Keep track of the medications / vaccinations advised for the baby once at home.

You're concentrating on your baby now, but remember that you have special needs, too. Taking good care of yourself will help you take the best care of your preemie.

Allow plenty of time to heal. You might need more time to recover from the rigors of childbirth than you imagined. Eat a healthy diet, and get as much rest as you can. When your health care provider gives you the OK, make time for physical activity, too.

Acknowledge your emotions : Expect to feel XXXXXXX sadness, anger and frustration. You might celebrate successes one day, only to experience setbacks the next. Give yourself permission to take it one day at a time. Remember that you and your partner or spouse might react to stress and anxiety differently, but you both want what's best for your baby. Keep talking and supporting each other during this stressful time.

Accept help from others. Allow friends and loved ones to care for older children, prepare food, clean the house or run errands. Let them know what would be most helpful. Surround yourself with understanding friends and loved ones. Talk with other NICU parents. Consider joining a local support group for parents of preemies, or check out online communities. Seek professional help if you're feeling depressed or you're struggling to cope with your new responsibilities.

To measure your premature baby's development, use his or her corrected age — your baby's age in weeks minus the number of weeks he or she was premature. For example, if your baby was born eight weeks early, at age 6 months your baby's corrected age is 4 months.

Regarding your question on development of preterm babies compared to normal ones, please go through the following link in detail :

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I think it would help you a lot.
In the summer season, keeping a fan on in the room is alright, as long as you do not have simultaneous air conditioners on, and the temperature does not drop too low.

Again, I would recommend the following link :

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Regarding bathing, you can definitely bathe him.

Just as you would gather supplies before making your favorite recipe, get your bath assembled in a warm environment. Most bathrooms are warmer than drafty kitchens, unless you mean to intentionally cool the baby.

Place the baby bathtub on a firm surface, and set your bath articles away from baby’s reach. Bath items you will want include a soft wash cloth, cotton balls, rinse water, etc.

Prepare the after-bath area for drying by padding with extra clean towels. To warm your towels before the bath, toss them into the dryer on the “delicate” cycle for 5 minutes or so. Never use a microwave or convection oven to warm towels or clothes.)

Your baby’s bath should be warmer than lukewarm, so he doesn’t get chilled. His body temperature is 98.6 F, so aim for bath water that’s between 99ºF to 100ºF. Test the water with your elbow, rather than your hand, as our hands are used to warmer temperatures. Remember to fill a non-glass container, like a large plastic pitcher, with warm rinse water before you begin.

If your baby’s umbilical cord has healed, you will dunk the whole body, except her head!, as opposed to a swipe n’ wipe. To place in the tub, spread your fingers and grasp the base of the skull and her shoulders with one hand. Use your other hand to support the lower body. Gently lower into the water. Concentrate on supporting the upper body and allow the lower torso to float freely.
Clean from top to bottom. Beginning with the eyes, wipe from the inner to the outer eye corners with cotton balls or a corner of a clean wash cloth soaked and wringed of plain water. Then change cotton balls, or rotate to another corner of the cloth. Avoid cross-contamination of any bacteria housed in one eye to the other as it’s easily transferred. With this in mind, also avoid back and forth swipes on the same eye.

Pay extra attention to the neck folds and creases in the arms and legs. Then, rinse using the plastic pitcher. It will be helpful to have an extra pair of hands!

When the bath is finished, lift your baby from the tub keeping the head and spine in alignment, and place on the back on those nice warm towels. Cover the body with a towel and dry quickly, blotting, into the nooks and crannies of the neck, arms, and legs.

You can use a cotton swab to dry behind the ear or in the curlicues of the outer ear, but avoid entering the ear canal except to soak up what moisture is visible. (A cloth wrapped around your finger may do just as well.)

Applying water to the head causes an immediate cooling effect. If your baby is feverish or the weather outside is hot, you may cool your baby with water to the head first. In most cases, plan to shampoo last.

The process of applying soap and doing an actual shampooing is not a daily need for baby (or most adults, for that matter). Once or twice a week should be sufficient.

Your baby will likely be fatigued and sleep longer after her bath. Plan to bathe about 30 minutes before the next feeding to avoid stomach upset. Preemie babies in particular need to digest while unstressed.

If you feel overwhelmed at the prospect of handling your preemie, you are not alone. Trust that you have grown to know your child and that you have the skills to parent him well.

I hope I have provided detailed information.
Take care, all the best, and feel free to ask any further questions.

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