Why does the Torah place the Mitzvah of Kibud Av va'Em on the first of the two Luchos (together with the Mitzvos Bein Adam La'Makom)? Why specifically here, after the Mitzvah of Shabbos?

What actions are included in this Mitzvah; and what is the difference between honoring parents and fearing them (Vayikra 19:3)?

Why is longevity the promised reward for honoring parents?

The Gemara (Kidushin 31a) tells us that the nations, upon first hearing the first few Dibros, could only remark that 'For His own honor He is sermonizing!' But upon hearing "Honor your father and your mother," they were forced to retract and concede regarding the prior Dibros as well. But why should we care what the nations say?