Is prayer nullified by having thoughts while performing it?
Prayer isn`t nullified by having thoughts while performing it, provided that the praying person offers all of its pillars and meets all of its conditions. However, the reward decreases significantly in the absence of reverence since a praying person is rewarded according to the attentiveness of his/her heart during prayer.
Is it permissible to pay the expiation of an oath to a charitable party as it feeds the poor and needy such as Tkiyet Um Ali?
There is no harm on authorizing someone to handle the expiation of another to the poor and needy, since Shafiee's jurists stated that authorizing someone for the purpose of distributing Zakah, expiation and vow is permissible as stated in [Mughni Al-Muhtajj,vol.3/pp.237]. At last, the intention of the person who intends to authorize someone else suffices in this regard. And Allah Knows Best.
Is it permissible for a woman to uncover her face while performing Umrah (minor Hajj)?
The woman while in a state of Ihram (ritual consecration) is obligated to uncover her face and hands, but at the same time permitted to let her head-covering garment drape from her head down over her face when non-Mahram (i.e., marriageable) men pass by her. And Allah Knows Best.
What is the Du`a (supplication) of Istikhara (guidance prayer)?
O Allah, I consult You as You are All-Knowing and I appeal to You to give me power as You are Omnipotent, I ask You for Your great favor, for You have power and I do not, and You know all of the hidden matters. O Allah! If you know that this matter (then he should mention it) is good for me in my religion, my livelihood, and for my life in the Hereafter, or he said: "for my present and future life" then make it (easy) for me. And if you know that this matter is not good for me in my religion, my livelihood and my life in the Hereafter, or he said: "for my present and future life" then keep it away from me and take me away from it and choose what is good for me wherever it is and please me with it."