Why did Moshe strike the rock and not speak to it?
Rashi and Rashbam: He erred. Refer to 20:11:2:1*. (because he was angry; 1 he erred in that he thought that he was supposed to speak to the rock by striking it. 2 On the other hand, since Hashem said "ve'Dibartem el ha'Sela", he decided that if the rock did not respond, he would speak to it 3 - Rashbam).
Bechor Shor and Rosh: Because that is what he was commsnded to do.
Why did Moshe strike the rock twice?
Rashi: Because the first time, since Hashem had not commanded him to strike it, it produced only drops. 1 In fact, first Moshe first spoke to the wrong rock, which of course did not respond. That is when Moshe and Aharon decided that perhaps they were supposed to strike it - like the first time in Refidim; See Sh'mos 17:6. The correct rock then appeared in front of him and he struck it.
Ramban #1 (citing the Ibn Ezra): Because, due to the people's quarreling, he became angry and struck the rock instead of speaking to it. He then controlled himself and struck it again with Kavanah, and water came out. 2
Ramban #2 (citing the Sifri): Because the first time, only a few drops emerged, because he struck it with anger. So Moshe and Aharon agreed to strike it a second time. 3
Targum Yonasan: Because the first time he struck it blood came out; 5 the second time, a lot of water emerged.
Rav Avraham Lapin: Refer to 20:12:1:9.
Riva: He means that at first only drops came out, since he was supposed to speak to it, and not to strike it. Moshe and Aharon realized that they were not commanded to strike and thought that they had erred about the rock. They spoke to a different rock, and thought that they must hit it, like earlier in Refidim. Moshe erred due to anger, like Rashi writes later in 31:21.
See Ramban's objection to this explanation (DH 've'Ta'anos Rabos'.
This also explains why Hashem punished Aharon too.
The Rashbam himself explains that he interpreted Moshe?s sin in this rounabout way, because he knew that Moshe can only have sinned by mistake and not on purpose.
Why does the Torah insert the word "va'Yetz'u Mayim Rabim"?
Rashi: Because the first time he struck it, only a few drops came out. 1
A commentary that is ascribed to Rashi (on R. Eliezer ha'Kalir's request for rain): Much water emerged from the rock and drowned those who complained.
Refer to 20:11:1:1*, 20:11:1:3.
