The origin and the meaning of "Abstract Syntax Tree"
You are asking three questions.  I will answer one.

I don't think "abstract syntax tree" is a misnomer.  It aims to represent the syntax of the expression.  It is not claimed to represent all of the meaning (semantics) of the expression.  The issue with bound variables that you mention relates to semantics rather than syntax.

Also, remember that names are merely that: references to some concept, to serve as an aid to communication.  Sometimes the concept is subtle or nuanced enough that no name is going to fully represent all the complexities of the concept, so we choose the best name we can (while keeping it fairly short).  And a name is just an aid to communication, so not all concepts have a fully precise, rigorous definition -- if it is used in a way that aids understanding and facilitates communication, that is often  OK.