This is sort of two separate questions, both of which require more than a quick forum post.
To learn about baptism, including the baptism of infants, the CCC (for brevity only posting a bit, I suggest reading the entire article):
http://www.scborromeo.org/ccc/p2s2c1a1.htm
The Baptism of infants
[1250] Born with a fallen human nature and tainted by original sin, children also have need of the new birth in Baptism to be freed from the power of darkness and brought into the realm of the freedom of the children of God, to which all men are called.50 The sheer gratuitousness of the grace of salvation is particularly manifest in infant Baptism. The Church and the parents would deny a child the priceless grace of becoming a child of God were they not to confer Baptism shortly after birth.51
1251 Christian parents will recognize that this practice also accords with their role as nurturers of the life that God has entrusted to them.52
1252 The practice of infant Baptism is an immemorial tradition of the Church. There is explicit testimony to this practice from the second century on, and it is quite possible that, from the beginning of the apostolic preaching, when whole “households” received baptism, infants may also have been baptized.53
For the next, children who die without baptism:
[1261] As regards
children who have died without Baptism , the Church can only entrust them to the mercy of God, as she does in her funeral rites for them. Indeed, the great mercy of God who desires that all men should be saved, and Jesus’ tenderness toward children which caused him to say: "Let the children come to me, do not hinder them,"64 allow us to hope that there is a way of salvation for children who have died without Baptism. All the more urgent is the Church’s call not to prevent little children coming to Christ through the gift of holy Baptism.
Last, read the article about the Church and non-Christians start at para 839:
http://www.scborromeo.org/ccc/p123a9p3.htm