Is a young man's estrangement from her considered a repentance for which she will be rewarded, and is it permissible to sell a gift from him and donate its price to her sister, who is married to a poor man, by saying, "I found it in a public place"?

Since the questioner is remorseful and determined not to return to forbidden speech, her repentance is valid. She must dispose of the forbidden gift by spending it on charitable causes and for the benefit of Muslims. It is permissible to give it to her needy sister without informing her of its source, using allusive language (tawriya) without outright lying. She will be rewarded for her repentance, not for giving charity with this money.