1. It is obligatory for the Imam to protect the prayer of those who are praying behind him from becoming invalid and to remember the number of Rak`ahs; he should not peck in the prayer (i.e., move too quickly), which undermines the pillars of the prayer, and he should not fall short in fulfilling the conditions of the prayer; he should make sure that he does the Sunnahs and postures of prayer properly, and so on. 2. The Imam takes on behalf of those who are praying behind him the responsibility of reciting out loud in the prayers where recitation is to be done out loud, and the responsibility of reciting the short Surahs (after Al-Fatihah) too. He also covers the mistake of the one who prays behind him if he omits some of the Sunnahs and even if he omits reciting Al-Fatihah if he comes late to the prayer. 3. The Imam is responsible for offering supplication for all those who pray behind him if he says Qunut or offers supplication for them. He is responsible for teaching those who prayed behind him the rulings on prayer so that it will not be spoiled and they will not be deprived of the full reward.

If the woman is one of your Mahrams, there is nothing wrong with you leading her in prayer and it will be counted as prayer in congregation. But if she is a non-Mahram, and if your leading her in prayer means that you will be alone with her, then in this case your leading her in prayer is prohibited.

1- When a person prays behind an imam, four scenarios may apply: 1- doing a movement before the imam, 2- delaying in following the imam, 3- doing an action simultaneously with the imam, and 4- doing a movement immediately after the imam. 2- Following the imam is the Sunnah and what it means is that a person starts to do the actions of prayer immediately after the imam starts them, but without doing them at the same time.