To your first question, no, as the spiritually dead need regenerating and I do not believe Scripture teaches infants are spiritually separated from God. Their natures, yes, as it has been appointed unto man ONCE to die.
If it's yes the only way a spiritually dead person is saved is by grace through faith. They must be saved in like manner
Then these babies get to heaven apart from the blood of Christ.
Christ died for sin- if these babies are not sinners then Christ did not die for them.
Therefore you have billions of people- the vast majority of the human race in heaven- you have them there without Christ.
More babies and small children die every day than adults. If all babies go to heaven, as I believe they do, but if they go to heaven because they are not sinners- then Christ saved a small minority of the human race that makes it to heaven.