My question is about 2 things:1) A situation in which twins are born, but attached together. One baby's heart is not pumping, but the second baby's heart is pumping for both. It wouldn't be advised by doctors to leave them together because the second child's heart will weaken and die. So my question is what would be the best thing to do.2) About abortion, when is it allowed and when is it restricted in the religion of Islam.

Praise be to Allah, the Lord of the Worlds; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.

It is known for every Muslim that the life of a human being should be honored, respected and protected, and it is obvious that the soul of the person has a high rank in the Islamic Sharia. In fact, Islamic Sharia came to bring forward benefits and complete advantages for human beings, as well as to ward off and reduce causes of evil.
Thus, we state that if it is possible for these twins to live safely by one heart, it becomes Haram to separate them if such separation may lead to destruction of one or both. And if it is not possible for them to live by one heart, i.e. they will die one after the other; here we are to wait until one of them breathes his last if this does not lead to instant death to the other before separating them.
But, if expert reliable doctors of medicine believe that the first one cannot live after the other, or their lives will be in danger if not separated , or the first cannot live originally in his present state, here - Allah knows best - it becomes legal to separate them to save one life, one person. This opinion is based on the Islamic norm that allows us to commit the lesser of the two evils. This norm is recognized by all Muslim scholars.
In addition, the life of the first one is not steady. This state is called in Fiqh terms al-Hayat al-Must'arah (the mock or artificial life). According to al-Muqirri al-Maliki: 'This life is like nothingness or nihility' .
As a result, if these twins cannot live by one heart and if we leave them in the same state, they will die, it becomes lawful to separate them as mentioned above.
For more details on abortion check our Fatwa: 81263 and 83814.
Allah knows best.