Is it permissible to slaughter one animal as a sacrifice and an Aqeeqah (the sheep slaughtered on the seventh day from the child`s birth)?
It is impermissible to do so since each of them is slaughtered for a different reason.
Is it permissible for a woman to offer the obligatory prayer after Adhaan (call for prayer), and before Iqamah (The announcement that the prayer is about to begin) in the mosque?
Yes, it is permissible for a woman to offer the obligatory prayer immediately after the Adhan and before the Iqamah in the mosque. And Allah Knows Best.
Is washing both openings (Istinjaa`) a must before every ablution?
Washing the front and back openings (Istinjaa`) is a must in case they have an impurity, but if they do not, there is no need for that, and Istinjaa` is not a condition for the validity of ablution.
There is a car dealership, and their method of selling is as follows: The customer pays the full price of the car, the car is registered in their name, and another contract is written in which the company commits to refunding the full price of the car to the customer after one year from the purchase date. What is the Islamic ruling on this transaction?
As for purchasing the car, paying its price, and owning it, this is a valid sale with no issue. However, the condition of refunding the price — whether the car is returned to the seller or not — is an invalid condition that nullifies the entire contract. Therefore, this transaction is invalid and not permissible. And Allah Knows Best.