Is thinking about proposing to a girl one has only spoken to in childhood, without having spoken to her since, considered reprehensible? And was sending her books a mistake?

There is no harm in merely thinking about proposing to a girl in the future, as long as it does not lead to a Sharia-forbidden act, such as imagining her beauty. It has been reported that "the adultery of the eyes is looking, the adultery of the tongue is speaking, the soul wishes and desires, and the private part confirms all of that or denies it." There is no sin in sending her books; in fact, the doer may be rewarded for it, as it is an act of kindness. One should adhere to modesty and chastity until Allah facilitates marriage.