Is it true that Saudi Arabia prohibits charging interest? What about UAE? Are there any states actually prohibit interest rates?
In Saudi Arabia, it is legal to charge (and pay) interest. However, according to this source, a contract clause requiring interest is not enforceable. An interest clause is severable, so the contract is not at risk if interest is charged. This source indicates an exception, that the Saudi Arabian Monetary Authority Banking Disputes Settlement Committee may enforce interest clauses in banking transactions. In UAE, Article 204 of the UAE Civil Code says
If the subject matter of the disposition or the consideration therefor is money, its amount and type must be specified without any increase or decrease in the value of that money at the time of payment having any effect.
and Art. 714 says
If the contract of loan provides for a benefit in excess of the essence of the contract otherwise than a guarantee of the rights of the lender, such provision shall be void but the contract shall be valid.
Art. 76 of the Commercial Code explicitly allows charging interest for commercial transactions
A creditor shall have the right to demand interest on a commercial loan in accordance with the rate stipulated in the contract. If the rate of interest is not stipulated in the contract it shall be calculated in accordance with the rate prevailing in the market at the time of the transaction on condition that in this case it should not exceed (12%) per cent, until full settlement is made.
This article from 2002 (behind the paywall, sorry) provides further analysis for Abu Dhabi. This page discusses similar rules for Kuwait, where again commercial transactions are exempt from the civil prohibition against interest. It is not clear where the line is drawn, but I think "commercial" refers to borrowing money for a business purpose, as opposed to buying your house.