The weekly readings of the Parsha, are they from the parsha of the just passed Shabbat or the just coming Shabbat? When we say this "week" is Parshat so&so , we mean the passed Shabbat or the coming Shabbat? And,....why....? (i.e . why not the other way?)

Shalom, Thank you for your question. As your question indicates, apart from the parsha reading in synagogue on Shabbat morning, we also read a section from the Torah during the week. The Torah is read during the morning service on Mondays and Thursdays, as well as at the afternoon service of Shabbat. On Shabbat afternoon we read the first section of the following weeks parsha (we divide the first "call-up" into three parts, and honor a Cohen, Levi then Israel with be called up to the Torah reading at the mincha, afternoon, service). On the following Monday and Thursday we read the same section again during the morning service. So, all in all, we read the first section of the parsha four times each week (Shabbat afternoon, Monday and Thursday morning, and again as the first call-up on the following Shabbat morning). Also, generally when we refer to the parsha of the week, we mean the parsha we will be reading the next Shabbat. My guess as to the reason for this is because we should always be looking forward! Blessings.