A person should only be baptized when he or she is old enough to consciously do so, and only after choosing to accept Jesus as their Savior. Being baptized is a symbol and public declaration of their decision to follow Jesus.
Yes. American Baptists do not have infant baptism. They see the baptism ceremony as a way for a person to publicly demonstrate their faith and be welcomed into the church.
Sure it is. Many Baptists believe that baptism must be an act of your own will, and that an infant can't decide for himself or herself whether to accept Christ, so baptizing an infant would be pointless.