Is it permissible to offer Tahajjud prayer after Witr prayer?
It is permissible to offer voluntary prayer after Witr (An odd number prayer performed between Isha and Fajr) prayer. However, it is desirable that the night prayer be ended with Witr. Therefore, it is desirable for one, who thought that he was most probably going to wake up at night in order to offer Tahajjud, to offer Witr after it, but one, who fears that he might not wake up, should offer Witr before going to bed.
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.
Is the son of the sister by breastfeeding considered a mahram in Islam, and is it permissible for a woman to go for Hajj with him?
Everything that is prohibited by lineage is also prohibited by breastfeeding. The son of the sister by breastfeeding is considered a mahram, just like the son of the sister by blood, and it is permissible for him to be her mahram for Hajj and Umrah. And Allah Knows Best.
Is it permissible for a young man and a young woman to enter into a covenant as a married couple without having a true seclusion (Khalwah) until their marriage contract is officially concluded?
The relation which isn`t based on a marriage contract is forbidden, and entering into a covenant as a married couple is unaccounted for and is from the evil suggestions of the devil.