Is it permissible for a woman in her menstrual period to recite from the Mus-haf (copy of the Quran ), or to recite by heart?

A menstruating woman is permitted neither to recite nor to touch the Quran according to what Ali Bin Abi Talib (May Allah be pleased with him) reported about the Prophet (PBUH) who was only held from reciting the Holy Quran by Janabah (Major impurity) [Al-Tirmizi in a sound Hadith]. Although Janabah and menstruation are major impurities, a menstruating woman is permitted to supplicate Allah (Duaa`) and make Zikr (Tasbihat ), even if these involved saying words from the Holy Quran, provided that she does not mean the words for themselves but as a supplication, or Zikr. Moreover, she is rewarded for not reciting the Quran during her menstrual period because she abided by the injunctions of Allah.

I took a car from the Orphans' Fund Development Institution; is there usury (Riba) involved in this transaction?

If the Sharia's conditions were met, then there is no harm in this. And Allah The Exalted Knows Best.

What is the ruling of Sharia on transplanting kidneys bought from another country because there are no donors from amongst the relatives of the patient?

How should a woman make up prayers that she missed two days from delivery?

All perfect praise be to Allah,The Lord of The Worlds                                                                                                                                                                        It is prohibited to delay prayer beyond its prescribed fixed time, therefore, the woman in question is obliged to make up missed prayers after delivery and confinement i.e. once she becomes ritually pure. And Allah Knows Best.