What is the source of the word, "Shamayim"?
Rashi: 'Sa Mayim' (it carries water), or 'Sham Mayim' (there is water there), or 'Eish u'Mayim' (which Hashem mixed together to form the Heaven). 1
The Ramban explains that Rashi follows his earlier explanation (to 1:6), in which case the Shamayim here is the same Shamayim as that mentioned in 1:1. The Ramban himself takes on that the Shamayim mentioned there is the Heaven above the 'Chariot' - about which the Torah offers no details (due to its spiritual nature - just as it does not describe the angels). The Shamayim here on the other hand, refers to the sky (the celestial sphere with which we are acquainted). From now on, the first Shamayim is referred to as 'Shemei Shamayim.' The Rashbam too, makes the same point.
What is "Yom Sheini" referring to?
Yerushalmi Rosh Hashanah, 1:1: It is referring to the Creation - not to the days of the week, to which the Torah never refers.
QUESTIONS ON RASHI
Rashi writes: "Hashem called the firmament (Raki'a), 'heaven' (Shamayim) - [This name means] 'carries water;' 'water is there..." What is bothering Rashi?
Gur Aryeh: The word 'Raka' means 'to flatten out,' so we understand why the name "Raki'a" is fitting. So why did Hashem rename it "Shamayim," a word which seemingly has no inherent meaning? Rashi therefore explains its etymology.