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.

I`m a cashier at a branch of the Civil Service Consumer Corporation. Sometimes, customers pay more than the due amount. Do I have the right to take that extra money knowing that I cover shortages from my own salary?

Does fasting on behalf of a deceased person permissible?

Fasting on belhaf of a deceased person is permissible, since the Prophet (PBUH) said: "Whoever dies while he still has some fasts to make up (of the days of Ramadan), then his heir (any of them) should fast on his behalf." [Agreed upon]. The previous answer is for making up missed obligatory fasts on behalf of the deceased. But if the fasting on behlaf of the deceased was for performing  a voluntary acts of devotion such as fasting....is permissible as adopted by the majority of Muslim scholars and based on the above hadith as they stated "Every good dead intended to be on behalf of the deceased its reward will reach the latter." And Allah Knows Best.  

What is considered a woman`s Awrah (parts of the body that must be concealed during prayer) while offering prayer, and is her foot part of it?

A woman`s whole body is considered an Awrah while offering prayer except the hands and the face. Thus, her foot is an Awrah as well. And Allah Knows Best.