What is the ruling on financing car purchases from Bank Al-Bilad based on the mentioned procedures, and is it considered compliant with Islamic Sharia?

There is no harm in obtaining financing through the bank selling the car after possessing it and selling it to you on a deferred payment basis, then you sell it to a third party other than the bank or the dealership, provided that the contract is free from late payment penalties and that the bank adheres to Sharia guidelines.