I agree with you that Jesus died to atone for our sins, and that infants are born with that propensity to sin- Catholics call it original sin. It is a state in which we are born, not an act we commit ourselves. I interpret Paul's “all have sinned” as all having committed personal sin themselves; “sinned” suggests action, at least to me; original sin requires no action; you are born with it!
Again, I do not see the logical connection that because babies sometimes die, and the wages of sin is death, that babies are therefore sinners.
The Catholic Church also hopes that unbaptized babies are saved, and entrusts them to the mercy of our loving Father.
It doesn't say that, it says in so many words that they were removed from the world and did not die. The Bible also say it's appointed to man once to die, and so they will. I realize the Catholic Church does not put much emphasis upon the book of Revelation, and what emphasis there is, is something with which I most frequently disagree, but the reference I made was to that book.
Many have studied the matter, it's a very striking chapter in a very striking book. The "two witnesses"... ponder the meaning of the word "witness" in matters both temporal and spiritual. Reading this, it's evident that there are no longer believers in the world, and these two witnesses are despised and feared.
Candidates for the two have been Moses, Elijah and Enoch, in the estimation of every theologian or speculating layperson I've encountered. Elijah appears to be almost universally accepted among those who have studied it, as one of the two. Moses, we are told in the Bible, died. To me, this means Moses cannot be one of the two. I do not believe in reincarnation; it's not scriptural. So, we have Elijah and Enoch as the two witnesses of Revelation. This I was taught by the numerous Protestant denominations to which I have been exposed.
According to the Bible, these two are physical men, witnesses, both literal witnesses testifying and spiritual witnesses, to the world without the Church, the body of believers having been removed, taken up, just as Elijah and Enoch were. This is a reasonable interpretation of what has been written there. Elijah and Enoch are also recorded as prophets, I believe once and future as well, fearsome ones with much power granted them in the world for that short time.
So, they didn't/wont die in heaven, they'll die their appointed death as all men are appointed once to die, here on Earth. And yet, they will be resurrected after the third day, so the hostile, unbelieving world will know. They will know, just who they are and just who sent them.
The remainder of your reply, I really don't see anything substantial enough as far as disagreement to hash out to any great extent. The wages of Adam's sin were death and all his descendants have been subject to it without exception. Infant baptism, in my view, is certainly a harmless act of faith taken in and of itself, but misguided since baptism is clearly a conscious act entered into by believers and infants are not capable. Later in life, I'd be concerned about the matter for those baptised without assent or even understanding. There's potential harm there. That is the reason I take issue with infant baptism.