Why is the 'Yud' missing from "Va'ashlichem"?
Ba'al ha'Turim (citing the Yerushalmi in Ta'anis, 4:5): To teach us the Aseres ha'Dibros flew out of the Luchos (when they entered the vicinity of the Eigel ha'Zahav).
Why did Moshe insert the breaking of the Luchos here?
Ramban #1: As part of the series of sins for which Moshe is rebuking Yisrael, he is pointing out the severity of the Chet ha'Eigel, to the point that, when he saw the people rejoicing before the Calf, he could not restrain himself from breaking the Luchos. 1
Ramban #2: To inform them how he had been Moser Nefesh on their behalf, by breaking the (Divinely-written) Luchos for their good. 2
Ramban: On any event it was necessary to mention it, in order to tell them about the second Luchos (at the beginning of chapter 10).
Ramban (citing Midrash Rabah): 'It is better for them to be judged as 'a Besulah' (by destroying their Kesubah) than as 'an Eishes Ish'. (And Hashem thanked Moshe for breaking the Luchos. See the last Rashi in the Torah and Targum Yonasan later on 10:1).
Why does the Torah insert the phrase "Va'espos b'Shenei Luchos"
Or ha'Chayim: Initially, the Luchos held themselves, 1 and it is only when they came in the vicinity of the Eigel that Moshe needed to grab hold of them to stop them from falling.
Moshe needed to hold on to them firmly in order to hurl them down with force and smash them. 2
As the Torah indicates n Pasuk 15, where it writes "u'Sh'nei Luchos ha'B'ris al Sh'te Yadai".
In spite of some commentaries, who explain that the letters that were engraved on the Luchos made them lighter and enabled Moshe to carry them, and that, when the letters flew away, they became too heavy for him to hold and he dropped them. The word "Va'ashabrem" however, implies that he threw them down forcefully.