What is the ruling on shouting at family members with the intention of advising them? Is refraining from advising them considered a sin? And is it sufficient to condemn evil in one's heart upon hearing backbiting or other major sins?

A caller to Islam must embody the characteristics of the Messenger of Allah, peace and blessings be upon him, such as gentleness and leniency, for Allah loves gentleness and grants for it what He does not grant for harshness. As Allah commanded Moses and Aaron to speak gently to Pharaoh. One must not raise their voice at their parents, no matter the justifications, and it is not permissible to remain silent about evil unless one fears harm to themselves, in which case they should suffice with condemning it in their heart.