This is a widespread myth.   SQL is an imperative language whose domain is (mostly) relations rather than lower-level objects.  It is only "declarative" in the sense that C is declarative: you tell the compiler what you want done, and it chooses an execution plan for doing it, namely a machine language program.

As for "procedural", it seems nowadays to be a synonym for "imperative".

Yes, if it is compiled; no if it is interpreted.  This distinction is meaningful but relative: languages are in all cases compiled into something lower-level which is then interpreted, whether by hardware or software.  We call an implementation an interpreter if it does only a small amount of compiling; we call it a compiler if the interpreter is hardware or very low level.

 

On modern pipelined CPU the so-called "machine language" is also smoke and mirrors.  "You don't fool _me_, young man.  It's turtles all the way down."