Asslamu Aleykum Wa Rhametulahi Wa Berekatu,
....how does Islam look at people born with handicaps or things like this?...
I think Brother Fi_Sabilillah has gone into a nice bit of detail in order to responde to your question, I would just like to add a couple of Ahadeeth which I have come across when reading on this topic, I hope they help.
The Brother mentions:
“Whatever befalls a Muslim of exhaustion, illness, worry, grief, nuisance or trouble, even though it may be no more than a prick of a thorn, earns him forgiveness by Allah of some of his sins.”
Also I would like to add a very similar Hadeeth on this topic, of which there are a handfull which I have seen.
Patience is entrusted and is one of the important aspects of a Muslim, in Bukhari's collection we read:
Volume 7, Book 70, Number 545:
The Prophet said, "No fatigue, nor disease, nor sorrow, nor sadness, nor hurt, nor distress befalls a Muslim, even if it were the prick he receives from a thorn, but that Allah expiates some of his sins for that."
So as to why people are created in such manners it could be this.
I had read a Hadeeth about a blind person or the reward of being blind. But I cannot find that, heres a beautiful hadeeth which shows the virtue of patience in such circumstances:
I found it in Muslim:
Book 032, Number 6245:
'Ata' b. Abi Rabih said: Ibn Abbas said to me: May I show you a woman of Paradise? I said: Yes. He said: Here is this dark-complexioned woman. She came to Allah's Apostle (may peace be upon him) and said: I am suffering from falling sickness and I become naked; supplicate Allah for me, whereupon he (the Holy Prophet) said: Show endurance as you can do and there would be Paradise for you and, if you desire, I supplicate Allah that He may cure you. She said: I am prepared to show endurance (but the unbearable trouble is) that I become naked, so supplicate Allah that He should not let me become naked, so he supplicated for her.
So we see, the Prophet peace be upon him, told her, I can pray for you, but Paradise will be with you if you are patient with your Illness, so she took the route of patience and paradise, but as a beautiful Muslimah she asked for her body not to be uncovered.
Also you went further on to ask, I think in response to Fi_Sabilillah's reply:
2. Allah has placed a physical law and a moral law in this universe. Allah allows suffering to occur when one or more of these laws are broken.
So does that mean that if a couple has a handicapt child they sinned?
And how is the child to perform the things promised mankind in Islam as a mercy?
If he can't even pray to his Lord? He can't marry or have children?
What did the child do to suffer in such a way? Or is the idea that the child does not suffer at all? And is still blessed somehow?
Even though Allah made him blind,deaf,and dumb?
I cannot see the number one point you made, but with regards to number two, it is not only when laws are broken but rather, it is a test, as shown, in the previous Hadeeth, the Woman's test was for her to be patient with her Illness, and thus she would enter paradise.
With regards to your other questions about if a Child can't do things or if a person who isn't totally sane can't do things I hope the hadeeth below helps to see those individual's place, and we also need to focous beyond this life, we see that a person who is patient in the face of Illness will be rewarded.
At this point I would jus like to mention a Hadeeth I have read in a Fatwa, I have not checked the reference, so please check it, since I have been lookin for a while now:
“The Pen has been lifted from three: from a child until he reaches puberty, from one who is asleep until he wakes up, and from the insane person until he comes to his senses.” Narrated by Abu Dawood, 4402; al-Nasaa’i, 3432; al-Tirmidhi, 1423; Ibn Maajah, 2041. classed as saheeh by al-Albaani in Saheeh Abi Dawood.
In the Light of all this we must also remember that, as I said before, we should not view the pain and sufforing here, as the final part, Islam teaches that the After life, is more better, and everlasting, Islam also teaches that:
The most miserable man in the world of those meant for Paradise will be dipped once in Paradise. Then he will be asked, “Son of Adam, did you ever face any misery? Did you ever experience any hardship?” So he will say, “No, by God, O Lord! I never faced any misery, and I never experienced any hardship.”
Saheeh Muslim, Again I do not have the exact number, someone maybe able to refer you to that if needed, INsha'Allah also if anyone finds the number please give me it.
So even someone who may have had Illness, or any type of pain, as small as a thron prick, they will be rewarded for it, and when, if, they go Paradise, the most mirserable man out of them will answer “No, by God, O Lord! I never faced any misery, and I never experienced any hardship.” when asked “Son of Adam, did you ever face any misery? Did you ever experience any hardship?” What about those less miserable than him.
I hope we all make it to Paradise, InshaAllah, and may Allah, grant us the patience of bearing through hardships, AMeen.
With regards to the Christian position, I have read a couple of Quotations, and they seem very nice, another thing I came across in my Christian days was a passage with regards to God punishin the kids for the Sins of the Parents, and a girl who preached in my college had a skin desise, and she said it was God punishin her because of her parent's sin or something, here is the passage:
9 You shall not bow down to them or worship them; for I, the LORD your God, am a jealous God, punishing the children for the sin of the fathers to the third and fourth generation of those who hate me, 10 but showing love to a thousand generations of those who love me and keep my commandments.
Source
Peace be upon those who follow truth when they see it, The Followers of Adam, Abraham, Noah, Moses, David, Jesus and Muhammad, Peace be upon all of them.
I hope this helped a little, anything I said wrong is my fault and anything good then Praise be to G-d.