What is "Ka'asher Tzivcha" here referring to?
Rashi (citing Sanhedrin, 56b): It (too) is referring to Marah, where Hashem first commanded Yisrael about Kibud Av va'Eim. 1
What are the connotations of the words "Ya'arichun Yamecha u'Lema'an Yitav lach ... "?
Ramban (in Yisro, Shemos 20:12) and Seforno: "Lema'an Ya'arichun Yamecha" refers to Olam ha'Ba (The world that lasts a long time), whereas "u'Lema'an Yitav lach ... " means that Hashem will also reward Kibud Av ... with a good life 1 in this world ... . 2
Kidushin 39b: They are in the world that is [totally] good and long, i.e. the world to come.
Tanchuma Ekev 3: They are both in this world.
Why did the first Luchos not contain "Lema'an Yitav lach"?
Torah Temimah (citing Bava Kama, 55a): Because they were destined to be broken. 1
And would have indicated that the Tov with which Yisrael was blessed would come to an end.
Why does it say here "Ya'arichun Yamecha", and regarding Shilu'ach ha'Kan it says "v'Ha/arachta Yamim" (22:7)?
Riva: The conjugation Ya'arichun means that others will cause this. If you honor your parents, they will pray that you live a long life.
In Bava Kama (54b), R. Chanina ben Agil asked why was "good" in the second Luchos, but not in the first, and R. Chiya bar Aba was unsure whether 'good' was said. Did he not know the verse?! And the Gemara concludes that it is lest 'good' cease from Yisrael, for the first Luchos would be broken. Why is there no concern lest "Ya'arichun Yamecha (your days will be lengthened)" cease?
Refer to Shemos 20:12:153:1.