Is it permissible to resort to the Jordan Islamic Bank to purchase a car, while having sufficient funds to do so, and to utilize those funds for other matters, and is there any Sharia doubt in dealing with this bank?

If the transaction with the Islamic bank for purchasing a car is permissible as a Murabaha (cost-plus financing) sale, then there is no harm in carrying it out, even if you are not compelled to, for Allah Almighty says: "And Allah has permitted trade." However, if the transaction is forbidden, such as an interest-bearing loan or stipulating an increase upon late payment, then it is not permissible for you to enter into it, because you are not in a state of necessity. What is forbidden is not permissible to commit except out of dire necessity, as Allah Almighty says: "And He has explained to you in detail what He has forbidden you, except that to which you are compelled."