You don’t. You give birth to your little one and then as the well wishers arrive, you introduce her. People will not know what to say. Help them out by giving them something to talk about. 

As parents introduce your baby. In the conversation introduce the problem and say something positive about your family and her, such as: "Here is Lucy, she has Down’s syndrome. She is sweet, she is making this difficult diagnosis easier to handle just by her sweet smile." Or "She wasn’t what we expected but now she is here we…" People will take their cues from your introduction and comments.

It depends on the reason. It is interesting you use the word scream. Is he bellowing to be picked up or played with? Is he becoming worked up before you respond to him?

If he is crying because he is teething, you will want to give him some infant pain reliever and rock him. Make sure he has the prescribed dose of pain reliever at bedtime when he is actively teething, if you want to sleep through the night. If he is yelling because he is lonely during the day, move him near you while you do your chores.

I always kept my babies within sight all day except while they were napping. Talk to him.  Take him out for airings in the stroller.  Make sure he has plenty of attention, lots of toys, and soothing music. All my babies enjoyed classical music. This is a demanding time on a mother. It will eventually get a bit easier.

I remember those days. With all four of my children I have followed the advice given in the book Healthy Sleep Habits, Happy Children (click on my bookshelf and you will find it)  Use it and re-read it whenever your resolve falters. This book turned all my children into sound sleepers and nappers until they reached first grade.  Why, I still put them down for a nap when I need one.