And similarly, "the second day" (= Monday) is Δευτέρα but "second" is δεύτερη (regular accent and ending).
The accent shift (and alpha instead of iota as feminine adjective ending after rho) are holdovers from Ancient Greek, which have been kept in the names of the days (that have become nouns), while as regular ordinal adjectives, the declension has been regularised.
I believe it's different for every country, to be honest. For French and Spanish, I do think that most days of the week are named after the planets of the solar system, and have nothing to do with numbers (If you of course exclude the words semaine and semana, that both have to do with the number 7) :)
In Israel the days are counted starting from Sunday ("Yom Rishon"- first day) followed by the second, third etc. With Shabbat as an exception (although while the meaning is unrelated directly, it does sound similar to sheva- seven). It was derived from the biblical week described in Genesis, 1
Σήμερα/today can be either an adverb or a noun. In this case, it is the subject of the sentence. Check out these dictionaries for documentation. You'll also note sentences similar to the one in the unit. "Today is Tuesday."
https://glosbe.com/el/en/%CF%83%CE%AE%CE%BC%CE%B5%CF%81%CE%B1 http://dictionary.sensagent.com/%CF%83%CE%B7%CE%BC%CE%B5%CF%81%CE%B1/el-en/ http://www.wordreference.com/engr/today http://www.dict.com/?t=en&set=_gren&w=today https://en.oxforddictionaries.com/definition/today http://www.merriam-webster.com/dictionary/today
Yes, indeed, in this case its function is a noun. Usually if it is a noun, it is accompanied by the article το. This is not the case. But usually is an adverb. Take a look at: http://www.greek-language.gr/greekLang/modern_greek/tools/lexica/triantafyllides/search.html?lq=%CF%83%CE%AE%CE%BC%CE%B5%CF%81%CE%B1dq=. I think it is the same in English for "today" , but with no article in any case for it.