How a Computer Represents a Number Electronically
An 8-bit integer is just stored in 8 flip flops.  A 16-bit one in 16 flip flops, and so on.  Most modern computers are 32 or 64 bit, so use banks of 32 or 64 flip flops for each register.

For speed, these are wired to other parts of the processor via parallel data buses. So entire "words" of memory can be transferred in one go.

There's no problem storing fewer bits.  If you run a 16-bit add on a 32-bit computer, it will just use 16 of the 32 bits it has in each register, and ignore the rest.  In a sense, it's the machine code instructions that define the meaning of the data.  The only difference between an 8-bit integer and an ASCII character is the way in which you choose to interpret the 8 bits.

Most computers use DRAM for their main memory.  That works in a different way, as a flip flip requires too many transistors.  A DRAM cell is essentially a tiny capacitor connected to a MOSFET.  The capacitor stores one bit (charged of discharged) and the transistor is used to read or write it.  Over time, the charge on the capacitor leaks away, so the memory has to be "refreshed" periodically, by reading each cell, then writing it back again to recharge the capacitor.

Hard disks store data in magnetic domains on the disk.  Magnetise a domain one way and it's a 0; magnetise it the other and it's a 1.  The data bits will be stored sequentially around the disk in tracks.  They are read or written as the disk spins round under the read/write head.