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 wearing a cap permissible for boys, or girls?
All Perfect Praise is due to Allah, The Lord of The Worlds.
In principle, anything is permissible sol long as there is no Sharia evidence prohibiting it, thus wearing the cap by boys is permissible as long as it isn`t done in imitation of the disbelievers. Moreover, a Muslim woman should avoid all that which attracts the attention of men because whatever leads to the forbidden is forbidden. And Allah Knows Best.
Is it permissible for a wife to give her money to her family as a charity, or a gift without asking her husband, or seeking his consent?
The wife has the right to give her money as a charity, or a gift to her family, or to other people after consulting her husband out of respect, and this is the meaning of treating on footing of kindness and equity. Therefore, if he wanted to stop her from helping her family, then there is no harm in not telling him.
Is it allowed to shave my beard to join the army taking into consideration that I can`t find a job?
All perfect praise be to Allah, the Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad, sallallahu ‘alayhi wa sallam, is His slave and Messenger.
The army should be joined in preparation for Jihad (Fighting in the cause of Allah), so if Jihad contradicts with growing a beard then it is allowed to shave it. And Allah The Almighty Knows Best.