Is one rewarded for giving a gift in Islam, and does a Muslim get recompense for it? And if someone gives away a very precious gift that was given to him, and then regrets giving it away, does he sin for that?

Giving gifts between siblings is commendable. Whoever intends thereby to help the needy for the sake of Allah will be rewarded for it. It is charity and maintaining kinship ties if the recipient is a relative. If the recipient is not needy, it is still a gift for which the giver is rewarded, in compliance with the guidance of the Prophet, peace and blessings be upon him, who used to accept gifts and encouraged his Ummah to do so. There is no difference whether the gift reached its recipient as a gift or if they bought it. Once it is accepted, the owner is permitted to dispose of it by selling, gifting, or giving it as charity. This is as the Prophet, peace and blessings be upon him, did when a silk garment was gifted to him, and he sent it to Umar ibn al-Khattab, saying: "I only sent it to you so that you may enjoy it," and in another narration: "so that you may sell it or clothe someone with it." So Umar gifted it to his polytheist brother. Regretting a gift is not commendable, and one should not give away what is dear to them unless they are highly content and patient. However, regret does not invalidate the reward if the gift was given with the intention of reward and recompense.