Thanks for mentioning it was in with other Mamluk coins. I checked Balog's Coinage of the Mamluk Sultans and found the second coin (with the square) was issued by al-Nasir Nasir al-din Muhammad, 3rd reign 709-741 AH / 1310-1341 AD.
The reverse (with the square) is missing most of the legend around the square that would indicate the mint and the year it was made. However, there are only three possibilities: Cairo mint from 720 or 721 H or Damascus mint from 720 H. In Balog's catalog these are numbers 242, 243, and 244 respectively.
Obverse legend:
صر
الملك النا
بالقاهرة
Reverse legend in square:
ية
سبعما
و
This appears as a line in the middle with something above and something below the line.
