Is this just the standalone version of "How?" or is it some other meaning of "How?"
Yes, it's how, but one meaning of how. This one is close to "like what?" "Làm sao" is how as in "how to do something."
"How" as in "In what way", then.... Got it.
Yes, it can stand alone.
Như thế nào = "like how" (như =like)
Làm sao = lit. make/do how