What is the ruling if hemorrhoid blood exits after completing ablution?
If this blood is exiting from outside the anus (due to the hemorrhoid protruding), it does not invalidate ablution, because blood exiting from the body from other than the two orifices does not invalidate ablution. If it exits from the anus (meaning from inside it), it invalidates ablution, and one must perform istinja' from it, wash the area of impurity, and repeat the ablution.
However, if this blood exits continuously such that no time remains sufficient for purification and prayer without it flowing, then it takes the ruling of urinary incontinence (sals al-bawl). One then cleanses from it after the time for each prayer enters, performs ablution immediately thereafter, and performs the obligatory prayer immediately. There is no liability upon him after that if something of it flows, and he may pray as many voluntary prayers as he wishes. If he wants to pray another obligatory prayer, he must cleanse himself and perform ablution. And Allah the Almighty knows best.
What is the ruling on buying a car from someone for less than the market price, because they are in a hurry to travel and want to sell their belongings at a lower price due to their urgency?
Yes it is permissible; however, a Muslim shouldn't take advantage of other's difficult situations.
Is it permissible for me to name my daughter "Leen"?
“Leen” means “ease”, and there is no harm in giving your daughter that name.
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.