The original 1963 version of ASCII covers some of this; a scan is available online. See also The Evolution of Character Codes, 1874-1968 by Eric Fischer, also easily found.
(It's also the only non-control ASCII character that can't be typed on an English keyboard, so it's good for creating WIFi passwords that your kid can't trivially steal.)
Don't count on it. There's a fairly long standing convention in some countries with some keyboard layouts that Control+Backspace is DEL. This is the case for Microsoft Windows' UK Extended layout, for example.
[C:\]inkey Press Control+Backspace %%i & echo %@ascii[%i]
Now replace "X" with "Delete".
Another good source on the design of ASCII is Inside ASCII by Bob Bemer, one of the committee members, in three parts in Interface Age May through July 1978.
I do understand that I've probably simplified "how I understand it" vs "how/why it was designed that way". This is pretty much intentional - I try to find patterns to things to help me remember them, rather than to explain any intent.