Is it permissible to offer Salah (prayer) on behalf of the sick who is on his/her death bed, and is incapable of offering it?
It`s impermissible to offer Salah on behalf of the sick, or the dead.
have an amount of 2,700 Jordanian dinars, which I have invested in a project, and I pay zakat on it every year. However, I have debts and obligations, and this project yields only a profit of about 2-4%. My salary is not enough to support myself and my family to the extent that I cannot pay the electricity bills. Is it permissible for me to take from the above Zakat?
You permitted to take from your Zakat since your income insufficient for you, because the poor is permitted to take from the Zakat in general, besides; the poor is identified of whose income doesn't suffice him. And Allah 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 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.