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.
Is a Muslim is Permitted to Pray Wearing Shoes?
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 There is no harm for a Muslim to pray wearing shoes or slippers so long as they are pure, since a man asked Anas Ibn Malik: "Did the Prophet (PBUH) use to offer the prayers with his shoes on?" He said: "Yes." Moreover, Ibn Rajab (May Allah have mercy on his soul) said: "Performing prayer wearing slippers/shoes is permissible according the majority of the Muslim scholars." [Fatih Al-Bary,vol.2/pp.274]. And Allah Knows Best.
Should one fulfill his vow of donating an animal to the poor and needy with one sheep although he had repeated the vow several times?
Each vow has to be fulfilled, and repeating the words of the same vow for confirmation renders its fulfillment obligatory as one vow. As for multiple vows, they have to be fulfilled as well.
Is washing the private part after urinating (Istinjaa`) a condition, and is it done with water and soap, or with water only?
Istinjaa` is obligatory for removing impurity, and it can be done with toilet paper, or a stone, or water. It is preferable to do Istinjaa` first with paper, or stone, or the like, then to wash the private part with water until making sure that the impurity has been removed. Using soap is not a condition, but there is no harm in doing so provided that it is washed off with water. It is also permissible to use either water, or paper if impurity is removed by any.