(1) Is  Boot  a small extension of Common Lisp with some non-functional
     features?

Boot is basically like common lisp just with another syntax.
Common Lisp is not functional. (setq a 5)

(2) Is this true that the Axiom mathematical library is compiled
     (in FriCAS) first into the Boot code  LibInBoot,  and this LibInBoot
     is not hidden, can be given and accessed by the user?

If I am not completely wrong, then spad is directly compiled to lisp and then the underlying lisp system compiles this into its native object format.

(3) In what language the Boot interpreter it programmed? In C ?

In a mixture of Lisp and Boot.

For library writer only SPAD should be relevant. One can access boot and Lisp functions, but using this in library code should only be done in very restricted places where one cannot do it by means of already existing library functionality. In fact, from some layer on the library should no longer know that LISP exists.

It would be totally bad design if you see LISP in a package that implements factorization of polynomials.

Ralf

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