I have 2 links of 1.5 mm f.o mm c / u I want to know if a transceiver GLC-GE-100FX would work for me, why and what are its variations.
The Cisco GLC-SX-MM for gigabit should be compatible with your 2960 - some vendors offer compatible SFPs using 1310 nm wavelength for 2 km MMF ("Cisco GLC-SX-MM-2K compatible").
Simply searching the Cisco web site produces the answer. According to Cisco 100-Megabit Ethernet SFP Modules Compatibility Matrix, that transceiver is compatible with your switch:
The GLC-GE-100FX uses MMF for up to 2 kilometers:
You need to make sure that 100BASE-FX is what you really want. That is a very old standard that is not well supported in modern equipment.