The different Hebrew and Greek terms that are translated as “(olive) oil” and “(animal) fat” in English are translated in Kwere with only one term: mavuta. (Pioneer Bible Translators, project-specific translation notes in Paratext)
Translation commentary on 2 Kings 4:5
So: The common Hebrew conjunction here serves as a logical connector and is rightly translated So in both Revised Standard Version and Good News Translation. Another option is to leave it untranslated as in New Jewish Publication Society’s Tanakh and Revised English Bible.
She went from him and shut the door upon herself and her sons: The woman then leaves the presence of the prophet and follows his instructions. But the text leaves quite a bit to the imagination of the reader here. She did not immediately go into her house and shut the door. Rather, she obeyed the order to send her sons out into the surrounding community to gather containers and then she closed the door. For this reason New International Version adds the word “afterward,” saying “She left him and afterward shut the door behind her and her sons.”
For shut the door upon herself and her sons, see the comments on verse 4.
As she poured they brought the vessels to her is literally “and they were bringing to her and she was pouring.” In many languages it will be necessary to say more precisely what was being brought to the woman and what she was pouring; for example, New American Bible has “As they handed her the vessels, she would pour in oil.”
Quoted with permission from Omanson, Roger L. and Ellington, John E. A Handbook on 1-2 Kings, Volume 2. (UBS Helps for Translators). New York: UBS, 2008. For this and other handbooks for translators see here .