Is it permissible to convert an amount of Saudi Riyals that reaches the Nisab into US Dollars before the Zakat due date to benefit from a better Dollar exchange rate, and does this conversion affect the Hawl (Zakat year) or the method of calculating Zakat if the funds are a mixture of different currencies?

Different currencies are combined to complete the nisab (the minimum amount upon which zakat is due), and their hawl (the lunar year period after which zakat becomes due) is calculated collectively, because they are considered of the same genus. So, if Saudi riyals are exchanged for US dollars, the hawl is built upon the original amount. Zakat becomes due when a full year has passed since the money was acquired. If you possess money in more than one currency, they are combined to complete the nisab.