what is an InnoDB Page checksum? What is an InnoDB Page checksum exactly? Does a Page checksum only detect issues with underlying storage when writing or reading to a page/block?
(I think this is what you are asking about.)

InnoDB "blocks" are 16KB.  But most disk subsystems work in smaller units -- 4KB or 512 bytes.  For InnoDB data to remain intact, the disk needs to write all 16KB as a unit -- either all written or none.  What can happen is that the pieces of the 16KB are written one after another, and the power fails part way through.  This causes a "torn page" ("page" referring to the 16KB block).

To recover from a torn page, InnoDB does two things.  It checksums each block in order to discover it, and it uses a "double write" for recovery.  The block (or at least certain critical blocks) are written twice - to some relatively constant spot, then to the desired location on disk (in the data or index).

When recovering from a crash, the "double write buffer" is checked to see if it leads to a "torn page"; in which case, it is repaired.

The double write, as its name implies, is costly.  (I have no metrics on how costly; I suspect the cost depends heavily on HDD vs SSD and RAID controllers.)  Turning it off is a way to gain some more speed, but with risk.  FusionIO was (it's been bought out) the only drive manufacturer who guaranteed 16KB atomic writes; I hope others have added this feature.

RAID with Battery Backed Write Cache should make the double write virtually zero cost.

A different checksum...  The Percona Toolkit uses a "checksum" for data.  Since rows are not necessarily laid out identically between Master and Slave, checksumming the files is not useful to seeing if the tables match.  I suspect it involves reading the rows in a repeatable order, and checksumming each row or clump of rows.

"rsync" does a similar thing, but at the file level.