What should one do who feels they have fallen short toward another person, and can they give charity on their behalf?

If the wrongs committed are injustices against others, then these injustices must be redressed or absolution sought from those wronged. If they are financial, then the money or its equivalent must be returned. If they are ethical, such as backbiting, then one should seek absolution for it and increase istighfar (seeking forgiveness) for the one who was wronged, and praise him. One can also perform a good deed and dedicate its reward to the one they wronged. Charity and supplication benefit both the living and the dead, by the consensus of Muslims.