Any attack made against a Face Down model results in an automatic Major Injury, so it isn't automatic - a model has to declare a Charge Action to take out another model in this fashion. The exception to this is the Close Combat fought at the beginning of a turn - this attack is "free", thus the Face Down model can be removed without taking an Action. If I'm understanding your scenario correctly, a model has Charged on its first Action, lost the Close Combat round and been placed Face Down. In that instance, you would be able to spend your second Action to Change State to Face Up, after which you'd immediately fight another round of Close Combat (at a -1 Att penalty). Mike will correct me if I've interpreted this erroneously.
In terms of your Resolve check question, yes, the Zombie would constitute a "new situation" and trigger another test. The poor agent has just come to terms with the existence of eldritch dogs - imagine his horror at turning and now finding himself set upon by the decaying undead! Rough day at the office, that.
Failing a last man standing check results in an Insanity roll. Just hope for Frenzy!