I don't think they'll try to kill eachother, not yet anyway. Kalona will probably try to milk the possession thing for all its worth, use it to cause a rift in Zoey and Stark's relationship, lure Zoey out in the open, and/or try to convert her somehow. Obsessed stalker, don't expect him to come up with a good plan.
I have no hopes for Kalona reforming, or Stark's relationship with Zoey. Not saying that neither of things won't happen, I'm not writing the books, but I honestly don't see how either could work out. Kalona is basically the worst kind of scum to walk this earth and no longer fit for the title of an angel. Meanwhile, Zoey and Stark barely know eachother but nevertheless are speeding through their relationship like they'll be dead within the month, up to the point where they've already sworn themselves into eachothers' lives, in a kind of permanent fashion, too or so Seoras says.