Is Zakat obligatory on a sum of 13,000 Egyptian pounds, knowing that part of it (5,000 pounds) was paid to reserve an apartment and has not yet been recovered, and is Zakat to be paid according to the Nisab of silver and not gold?

The lunar year, not the Gregorian year, is what is considered for Zakat (definition). The threshold (nisab (definition)) for wealth must be determined solely by the Hijri year. The nisab for Zakat on money in the form of banknotes or trade goods is estimated according to what is more beneficial for the poor, whether it be the nisab of gold or silver. So, if the amount equals a nisab of silver and a lunar year has passed without it falling below the nisab, Zakat becomes obligatory.