Yep, looks like the bike is scavenged together from ?hopefully not stolen? random parts.
The W-'womens specific design' quill it has came off a ladies department store schwinn
is that a v-brake I see? I hope the brake levers are linear pull; the original ones for a 930 arent...

yeah, don't get a quill adaptor; those are best used for when you have a threaded fork that *you want to keep* but still want modern stem selection

just ditch the fork; it's not a good one.
Get a threadless rigid fork (that bike is meant to be non-suspended at any rate, that random SR fork is probably offsetting the geometry)
things will be much cleaner