My Israeli friend explained to me that the word "שבת" is a feminine word, since the plural uses the feminine ending - it is שבתות.
If this is true, why is a common greeting שבת שלום ומבורך using the maculine format instead of שבת שלום ומבורכת ?
With respect to your friend, the fact that shabbat pluralises as shabbatot is itself insufficient for demonstrating that it's a feminine word. Lots of masculine words take that plural - such as אבות, for example - and some words can take both plurals (שמשים vs. שמשות, etc).
As it turns out, shabbat can function both as a feminine and as a masculine noun. An example of where a pronoun referring to Shabbat is masculine would be Isaiah 56:2 - שמר שבת מחללו (not מחללה). An example of where shabbat takes a feminine verb would be Leviticus 25:6 - והיתה שבת הארץ (rather than והיה).
According to the BDB, the word was originally feminine but came to be thought of as masculine because of the influence of the phrase יום השבת, in which יום is masculine.
[Note: to see a discussion of this word's functioning both as a masculine and as a feminine noun, look at Tosafot on Ketubot 5a (s.v. שמא ישחוט בן עוף).]