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 to donate corneas to Jordan Eye Bank or all the organs via telephone?

All perfect praise be to Allah, The Lord of The Worlds, and may His Peace and Blessings be upon our Prophet Muhammad and upon all of his family and companions.

Corneas donation that is carried out after one's death is permissible by the Board of Iftaa'. Because this procedure is highly sensitive, the donation process

should undergoes to an accredited mechanism. And Allah, The Exalted, Knows Best  

Does the time of Fajr (dawn) prayer start after the first Athaan (call for prayer), or the second one?

All perfect praise be to Allah,The Lord of The Worlds                                                                                                                                                                    The time of Fajr prayer starts after the second Adhan. And Allah Knows Best.

What is the ruling on performing Umrah after the latest expansion of the Mas`aa (the passage between As-Safa and Al-Marwah), is it permissible, or not?

Yes, it is permissible to perform Umrah after the latest expansion of the Sa`y area since making Sa`y between As-Safa and Al- Marwah is already observed. And Allah Knows Best.