Is the prayer of a woman who entered the mosque at the time of the Maghrib call to prayer, and prayed before the iqama, then during the second rak'ah the imam started the iqama, so she completed her prayer individually, valid? And is it obligatory for her to pray in congregation if she is in a hurry?

Congregational prayer is not obligatory for women. According to the Shafi'is and Hanbalis, it is sunnah for them to pray in a congregation among themselves, based on the actions of 'Aisha and Umm Salamah, and the Prophet's (peace be upon him) command to Umm Waraqah to lead the people of her household in prayer. On the other hand, the Hanafis dislike the congregation of women out of fear of fitnah (temptation/strife), and the Malikis prohibit it due to the condition that the imam must be male. A woman's individual prayer is valid. If she attends the mosque, it is better for her to wait for the imam to attain the virtue of congregational prayer.