Is it possible for a Muslim, who does not repent of his refusal to believe that Jesus is the Son of God, and that Christianity is the truest form of religion, to die in a state of grace and be saved? Yes, this is possible. Many Muslims die in a state of grace and are given eternal life in Heaven, usually after a purification in Purgatory. It is also possible for such a person to die and be sent directly to Heaven, without a stay in Purgatory.
Though it is an objective mortal sin to reject Christianity, it might not be an actual mortal sin, due to a reduction in culpability. The devout Muslim who does not realize that Jesus is the Son of God, but who has great respect for Jesus as a true prophet, may be in a state of invincible ignorance. And even if his failure to realize the truth about Christ and Christianity is culpable, it might not have the full culpability of an actual mortal sin. Therefore, a Muslim may well be in a state of grace. If he then dies in a state of grace — having no actual mortal sins of any type, unrepentant, on his conscience at death — then he will be judged by God and will have eternal life in Heaven.
At Medjugorje, the Blessed Virgin Mary was asked by a visionary, Who is the holiest person in Medjugorje? She replied that a particular woman, who is a devout Muslim, is the holiest. How can this be? Almost the whole town is Catholic Christian, and many priests and religious live there.
First, you must understand that the superlative in many languages, even to some extent in English, is not always the one who is above all others. The smallest, or the greatest, or the largest, or the holiest, can refer merely to one that is among the most, and not necessarily one that is singularly the most. For example, in English, I might say that you look most beautiful today. This use of the superlative is general, among the most beautiful, and not singular, the one that is absolutely more beautiful than any other. Similarly, when Jesus said that the mustard seed is the smallest seed, He meant only that it is among the smallest seeds (general superlative) and not absolutely smaller than any other seed (singular superlative). There are seeds that are smaller than the mustard seed, but Jesus’ assertion is still true, because the mustard seed is among the smallest.
Perhaps the questioner was asking (inappropriately) for an answer with the singular superlative. But Mary wisely answered with the same type of general superlative used at times by Jesus. She was teaching them something about holiness by pointing out that this Muslim woman is among the holiest. It is not the exterior acts that make one holy, but the interior. So a Catholic who lives at Medjugorje and is friends with priests and religious, and recites all the right prayers in all the right places, is not necessarily the holiest. Rather, she who is single-hearted in her devotion to God, is among the holiest.
Mary’s answer also implies that a Muslim who knows much about the Catholic Christian Faith, as this woman living in Medjugorje must have known, can still be in a state of grace, and therefore also can still be saved.
But of course, this does not imply that all Muslims are saved. Not all Jews are saved, not all Catholic Christians are saved, not all Catholic Bishops are saved, not all of the Twelve Apostles were saved (Judas, I think, was sent to Hell). A person does not automatically receive salvation by belonging to Catholicism, or by being a Bishop, or even by being an Apostle chosen by Christ. Each person is judged by God based on his life, especially whether he avoided mortal sin, or repented from any mortal sins that may have been committed.
Whoever dies in a state of grace, will have eternal life in Heaven. Whoever dies in a state of unrepentant actual mortal sin, will have eternal death in Hell. There are only two final resting places: eternal happiness in Heaven, or eternal unhappiness in Hell.
On the topic of children who die without baptism, see this article:
On the idea of a limbo of children in Hell