What is the expiation for being forced to give a false testimony in order to achieve reform?
Achieving reform is done by following the way of Allah through giving back rights to whom they belong. Therefore, repenting to Allah from false testimony is only achieved by abrogating it, and the person in question should expiate for that oath if he had taken it, so that Allah may forgive him.
Is it permissible for a Muslim woman to go out wearing adornment and not putting on her Hijjab (Islamic wear)?
It is impermissible for a Muslim woman to go out wearing adornment, and not having her Hijjab on.
Is it permissible for a woman to visit the doctor while in her `Iddah(waiting period)?
It is permissible for her to do that during day time, but it is impermissible for her to go out at night except for a sound reason.
Generally speaking, I`m dutiful to my mother and opt for obeying her. However, she chose a certain girl to be my future wife, but I`m not pleased with her choice although that girl comes from a good family and enjoys good character. Should I obey my mother or choose another girl that lives up to my expectations?
Praise be to Allah the Lord of the Worlds.
One must obey their parents in whatever is in compliance with the teachings of Sharia and within one`s capacity. However, you aren`t to blame for not marrying that girl, but it is better that you tell your mother about that and it is preferable that you perform Istikharah prayer. And Allah The Almighty Knows Best.