How data is stored in memory beyond 0s and 1s?
Digital data is generally stored as 1s and 0s at some level.  That is only the view of one level in a large layered hierarchy.  Below that you get into charges, phase change of material, mechanical dimples, voltages in active circuits, little regions of magnetic domains, and lots more ways people have come up with over the years to store bits (the 1s and 0s).

Above the bit layer there is a hierarchy eventually surfaced to applications as a file system by the operating system.  There are several layers above the bits and below the file system, but these vary depending on the exact storage device and the file system.

In general, large storage devices like disks, will present their memory as "sectors" or "blocks" that are the minimum amount that can be written or erased at once.  In flash drives there is a layer that does "wear leveling" that swaps around physical blocks to implement the logical blocks presented upwards.  Flash blocks have a limited write and erase lifetimes, and this layer seeks to wear them out as evenly as possible.  Magnetic disks don't have this issue, but do sometimes have a "bad spot" layer that avoids physically defective blocks from the logical blocks presented upwards.  Blocks usually contain CRC checksums implemented by the hardware.

The file system usually deals with the logical blocks directly.  It uses some as index to know what it stored in others.  Some file systems log operations to aid in recovery.  There are lots of strategies for knowing which blocks are used to store the content of which files, which blocks are empty, etc.  File systems often add their own checksums to logical blocks or files and other structures.

Eventually the file system presents a collection of "files" to the operating system.  The OS will usually define a few files for its own purposes, then present something a little different to applications.  How much different depends on the OS and whether it is intended to deal with multiple possibly hostile processes and other concerns.

Eventually the application sees arbitrarily sized collections of data, called files, it can read and write without having to worry about sectors, blocks, or how individual bits are physically stored.  Modern file systems tend to present files as named entities in a tree structure.

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