spring recruitment

No one could possibly know now. Only sororities who have space available will participate. (informally of course)

Only the ones that are under chapter total, which is a number that Panhellenic will set in a few weeks.

"Spring rush" isn't really a thing. If a house is just a few girls under total, they'll discreetly give out bids to close friends of actives. If a house is pretty far below total, they'll probably choose to have a few informal rush events that are by invitation only. You can put your name on the COB list with Greek Life, but there is no guarantee that you'll be invited to an event (should there be any events).

it really depends and there's no way to know now. sororities like dg, agd, and likely dphie always do spring bc so many girls drop out they want to keep their numbers up. these typically take a large number, like 10-15 girls. other sororities do spring rush but it's very under the table; getting invited to dinner, etc, usually only if you're friends with current sisters. these usually only take a few because certain sororities nationals require them to replace all the girls that graduated early to maintain quota. sigma kappa and dz and gamma phi took like 7 or 8, tri delt took 6, and chi o took 4.

Are PNMs that withdraw voluntarily ever offered a bid through COB?

You need to sign up for COB through Panhellenic.

Really, it's whoever has girls graduate, transfer, or drop after fall semester. And, sometimes, quota is raised and everyone has to add members. But.,even some who lose girls won't do spring rush. Some aren't required to, and others will quietly offer bids to known girls. There's no way to tell at this point, but it's usually a good mix of houses that have spaces to fill.
There's no truth to the rumor that houses that have spring openings are "bad" houses. There are soooo many reasons that spots become open.
Definitely sign up for COB so the houses that end up with spots know you're interested.