Is learning Tajweed obligatory, and is it permissible to read and memorize the Quran without Tajweed until circumstances are favorable for it, especially given the mother's current objection to learning Tajweed?

Reciting the Quran with proper tajwid is an obligation for both men and women. There is no harm in reading it without a shaykh, as long as this does not lead to altering the words or distorting the letters. If your mother prevents you from attending a Quranic instruction course, you can recite the Quran from the Mushaf and utilize audio and video recordings and discs.