Are ladies permitted to drive the car for social, domestic or luxury purpose?
If they observe shari’i pardah (veil), then they can drive car.
Is it ok for a girl to tell a boy that she likes him? If not, what should she do if she has already told him?
If the boy is that girl’s kufw (compatible to her) according to Islam and Shia Faith, then there seems no objection in expression of this fact as a result of which the two may get married. And Allah knows the Best and He is the Saviour!
Is it permissible for a woman to lead the congregation (jamaat) in which men are also following her?
A woman can lead other women in congregational prayers, but it is not permissible for a man to offer his prayers in a woman-led congregation.