Why do some Protestants wait until they are adults to get baptized?
The difference in our practices stems from the difference in our understandings of Baptism. Since the beginning of the Church, we have understood that Baptism actually affects us. It is something that God does to us. Protestants (in one way or another) have rejected the idea that the Sacraments actually do stuff to us. Depending on the denomination, they may be closer or farther from the full truth of what Baptism does, namely:
Because we recognize how amazing Baptism is, we want that for our children as soon as possible.
Many protestants think Baptism is something they do for God (an outward sign of their acceptance of Jesus). Since they don't understand that Baptism does all the above-mentioned stuff for us, they have no reason to baptize until they're older (when they can make an adult decision to accept Jesus).
They also don't find any explicit mention of baptizing infants in Scripture (though multiple times Scripture mentions whole households being baptized at the same time, Baptism clearly is the New Testament fulfillment of circumcision (which happened to babies), and we have explicit 2nd century texts on infant Baptism as a tradition of the Church). Despite these glaring examples, they hold to a strict sola scriptura mentality and reject the idea that infants can be baptized.
What about "re-baptism"?
Since, to many Christians today, Baptism is something they do for God, there's nothing (in their minds) preventing them from doing it again whenever they have fallen away from God and want to re-commit themselves to Him.
If, after Baptism, I want to re-commit myself to God and show remorse for post-Baptismal sins, I would confess my sins in the Sacrament of Reconciliation, and receive Jesus physically in the Sacrament of Holy Communion. Since protestants lack both of these, it is easy to see why "re-baptism" was invented.
"Re-baptism" fails to understand the unremovable mark on our souls--something that can only be given once, and cannot be changed. That is why the Nicene Creed states "I believe in one Baptism for the forgiveness of sins." I can only receive the mark on my soul once. Any future "baptism" is really just me getting wet.
What about Confirmation?
Confirmation is fundamentally different from the Protestant understanding of Baptism.
It is NOT the public act of the person "confirming" (affirming) that he wants to be Catholic, nor as some say "confirming one's life to Christ."
Confirmation confirms (strengthens) the graces we received in Baptism (something God does to us). In our diocese we confirm as early as possible (age of reason: about 7) because we want our children to have the advantage of those strengthened graces in their souls from as early as possible.
The Sacraments affect us. They are not merely outward actions that we do.