What should a person do about the elderly who commit acts that violate Islamic law and refuse advice, and should he continue advising them despite their objection and harshness, or should he stop?

Inviting to Allah Almighty is a great obligation, a virtue, and an act of closeness (to God). It is the function of prophets, messengers, and the righteous. The caller (Da'i) must be patient, and not become weary, weak, or despair, for calling (to Islam) requires patience and perseverance, as Noah (peace be upon him) did when he called his people for nine hundred and fifty years. The caller must also be gentle with the one being called and choose appropriate times, and he must seek Allah Almighty's help and supplicate to Him to guide the one being called, for Allah عز وجل is the Guide of hearts. Evidence for this includes the story of the conversion of Abu Hurayrah's mother (may Allah be pleased with her) through the Prophet's (peace and blessings of Allah be upon him) supplication.