Is it true that the Prophet, peace and blessings be upon him, forbade disclosing one's wealth, travel dates, and age? And what is the wisdom behind concealing one's age, if that is true?

There is no prohibition against stating one's age mentioned in an elevated (marfu') hadith. The decision not to disclose it is up to the individual, and there is no harm in that, as long as it does not lead to deception or fraud. Concealing secrets is considered a means by which a person achieves their needs, as the Prophet, peace and blessings be upon him, said: "Seek help for the fulfillment of your needs through concealment." It has been said that it is part of a man's chivalry not to disclose his age, and that wealth is among the things considered a secret. A Muslim should not embarrass his brother with useless questions or by inquiring about people's private matters.