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.
I suffer from absentmindedness and constant worries during prayer, what should I do?
You should take refuge in Allah from the whispers of the devil and life worries. You should also seek Allah`s help and offer a lot of Istigfar (seeking the forgiveness of Allah). And Allah Knows Best.
Should a woman who broke her fast because of delivery make up for missed fasting days before the next Ramadhaan, and what is the expiation due on her in case she delayed making up for them ?
She should make up for missed fasting days before the start of next Ramadan if possible, but if she didn`t while being able to, then she is obliged to make up for them along with feeding a needy person for each delayed day of the missed fasting days. However, if she wasn`t able to make up for the missed fasting days before the start of next Ramadan, she has to fast a day for every day that she missed, and no ransom is due on her. And Allah Knows Best.
Is it permissible to offer one Rak`ah in Witr prayer?
The minimum of Witr (An odd number prayer performed between Isha`a and Fajr) prayer is one Rak`ah, and the maximum is eleven, but the minimum of its complete form is three, and it is permissible to offer one only.