LB, I don’t get it- if you wrote a letter on Fri, then it has Friday’s date, why would anyone thing you wrote in on shabbos? (By the way, there may be an issue with putting the card in the mailbox right before shabbos if you know for sure that the mailman will pick it up on shabbos – it may be an inyan of amira L’goyim- asking a non-Jew to do a melacha for you; I am not sure, you wold have to ask a Rav about this, or one of the CRers will pipe up)
OP- why do you have to refer to any week, just use the date and the day. Motzei shabbos in actually Sunday (we just are reluctant to let Shabbos leave, so we still refer to it in terms of shabbos, even when it is over), it’s the first night of the new week, you date it with Sunday’s date if you are using the Hebrew date. ie Motzei Shabbos, 12 Elul, or Sun 12 Elul, or Motzei Shabbos, Sept 2. Are you asking whether you write, Motzai Shabbos Parshas Ki Tezei (meaning the Parsah read that morning) or refer to the coming week’s Parsah? I think since Motzai refers to the past shabbos, you can write the name of the Parsha that was just read on that shabbos (ie which shabbos was just over? Parshas Ki Tezei).