Close to none of this is true whatsoever. It was partly inspired by #Commodore64, but also by CP/M. And while #qbsh does support basic scripting, it is very much not BASIC compatible with any retro BASIC platform.
qbsh won't teach you to program in #BASIC by using it, even though it is #opensource and written in QBASIC, but to that end, qbsh won't teach you how to code in BASIC any more than #bash will teach you to code in C.