To the first question I lean towards no. However, that is a question only God knows. Just because one is baptized does not seal the infant to heaven. There is now baptismal regeneration and when we baptize our children we realize that they are sinners in need of the baptism of the Holy Spirit who is the seal of what baptism signifies.
To the second question Yes and no. But only God knows.
"There are two things suited to humble our souls of men. And they are, first a due consideration of God, and then themselves; of God, in his greatness, glory, holiness, power, majesty, and authority: of ourselves, in our mean, abject, and sinful condition."
John Owen, Indwelling Sin In Believers