Am I permitted to perform more than a prayer within single ablution?
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.
You are permitted to pray as many as you could within one ablution and to recite Quran so long as your ablution isn't nullified. And Allah Knows Best.
Is it permissible for a woman to visit the doctor while in her `Iddah (waiting period)?
It is permissible for her to do that during day time, but it is impermissible for her to leave her house at night except for a sound reason. And Allah Knows Best.
Is it permissible to offer Istikhara prayer (seeking guidance) after Witr Prayer (A confirmed Sunnah which is offered after Isha prayer and before Fajir prayer with a minimum of 3 Rak`as and a maximum of 11)?
It is permissible to offer Istikhara before and after Witr prayer as it is permissible at any time except that in which prayer is disliked. And Allah Knows Best.
A person owns sheep or goats and occasionally feeds them from the grass in other people's orchards without the owners’ permission. Is it permissible to eat the meat of these animals if invited to do so? Is it permissible to purchase from these sheep whose owner feed them from people's orchards without their permission, and can one accept gifts from them, such as meat or milk?
Yes, it is permissible because the one who is accountable is their owner, and the cost of the grass on his accountability. In addition, in order to be on the safe side you should abstain from eating his products, because his sheep case is as if they were fed on impurities. And Allah Knows Best.