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 person, who vowed to offer two Rak`ahs (units of prayer) everyday for Allah`s sake, to do so after the Fajr (dawn) prayer?
In principle, a vow should be fulfilled as it was originally intended, and if its time lapses then, it should be fulfilled at any time because of the vow. Therefore, it is permissible to offer them after the Fajr prayer, and there is no prohibition in doing so. However, it is preferable for him to offer these two Rak`ahs at some other time to avoid the disagreement amongst the scholars in this regard.
Is keeping money in and taking profits from the Islamic Bank lawful?
If Allah Wills this is lawful, because they stipulate on theselves to work in accordance to the guidlines of Islamic Law. And Alalh Knows Best.
Should the Zakah (obligatory charity) giver tell the poor recipient that this is the Zakah of his money?
No, he shouldn`t. But, the Zakah giver should make an intention in his heart that it is the Zakah of his money when paying it to the poor. And Allah Knows Best.