Why did Moshe opt to make the snake out of copper.
Rashi and Ramban #1 (citing Midreah Rabah): It is a play on words, since the snake is called Nachash, he made it out of Nechoshes. 1
Ramban #2: It is Hashem's way to perform a miracle within a miracle, by removing the punishment using the very same object with which He dealt the stroke. 2
See Sifsei Chachamim.
Ramban: See for example, Sh'mos, 15:25 and Melachim 2, 2:21 and see Yoma, 84a. See Ramban, who elaborates.
Presumably, the Pasuk refers to it as "Nachash" (even though Hashem told him to make a 'Saraf', as a play on wards (Nechoshes - Nachash).
Seforno: To drive home the message that they had copied the sin of the snake with the breath of their mouths by speaking against Hashem, against His work and against His servant (to galvanize them into doing Teshuvah). See also Ramban, the latter part of the Dibur.
Why does the Torah write "ve'Ra'ah Oso va'Chai" in Pasuk 7 and "ve'Hibit el N'chash ha'Nechoshes va'Chai" here?
Rashi: Because in Pasuk 7, the Pasuk is referring to those who were bitten by other animals, whose bites were less lethal and for which a mere glance sufficed to cure them, whereas the current Pasuk is referring to those that were bitten by the snakes, whose bites were lethal and who therefore needed to gaze at the snake in order to be cured.