What is meant by the phrase "entered into his responsibility" found in the condition "that the seller must have taken possession of the sold item and it must have entered into his responsibility before he sells it" in a halal Murabahah sale? Is the Murabahah sale to a purchaser permissible if the bank buys the car and it enters into its ownership, and then it sells it to me, or if the bank buys the car and it directly enters into my ownership?

The phrase "entered into his responsibility" means that the seller bears the responsibility for the destruction of the sold item before delivery, and the responsibility for its return if a hidden defect is found in it after delivery. If the bank buys the car and takes possession of it first, and then sells it to you, this is a permissible murabaha sale. However, if the bank lends you the price of the car with an increase, this is a prohibited usurious transaction, regardless of the name or whether the car remains mortgaged.