Learning Torah directly after Havdala:
It is a proper custom to begin one’s week with Torah learning and hence learn Torah immediately after Havdala. One who does so is assured to be successful in his Torah learning of that coming week.
May one recite Pesukim from Tanach on Motzei Shabbos?
Some write one may read Tanach on Motzei Shabbos until after Melaveh Malka, as the holiness of Shabbos is still upon him. However from the simple wording of the Poskim one is to avoid reading Pesukim of Tanach on Motzei Shabbos just like on any other weeknight.