Before Floppy disks were available, people still transferred data. It used to be with help of punch cards, reel to reel tapes, and cassette tapes. The early home computers used cassette tapes.
Floppy disks use a FAT file system.
Floppy disks use magnetic disk to store the data.
Magnetic
No. Zip drives cannot read floppy disks, and cannot be used on a traditional floppy controller.
Storing data, transferring data from on computer to another.
Magnetic Disks, otherwise known as 'Floppy disks'. The last generation of these disks were 3 1/2" and used a ridgid plastic case, to contain the magnetic disk within. Not very floppy. The early versions were 7" and 5" and were contained in soft plastic outer sleeves. These were actually floppy.
The best current way to proceed about this would be to just get a new floppy, as a broken is impossible to "fix" as floppy disks are way outdated now, because most people use flashdrives and CD-RW disc.
Modern 3.5" floppy disks were/are double sided. Earlier 5.25" floppy disks started out single sided but you could cut out a read only slot and flip them over and use both sides, no guarantees though. Even earlier 8" floppy disks were also single sided but could likewise be cut and flipped over. This is from my own experience not from research.
magnetic
mass
No. Several consoles used CDs before the PlayStation did. Examples include the Sega CD, Sega Saturn, and the Phillips CD-i. There was also a Famicom Disk System peripheral for the Famicom (the Japanese version of the NES) which used floppy-like disks.
CD's hold many times as much data as a floppy - 700 meg vs. about 1.44 meg. They're also cheaper to buy, less fragile and not susceptible to data corruption by magnetic fields.