Both of those can certainly happen. If there is a fence to fly over, there is always some chickens dumb enough to fly over it no matter what kind of danger lies on the other side. And there are BYC members have lots of stories about neighbor dogs who killed their chickens.
Welcome to BYC. Glad you decided join our flock. Be careful of your chihuahuas around your chickens as dogs and chickens typically do not mix well. We get lots of letters from new members who are horrified because their seemingly benign dog (even small breeds like chihuahuas) suddenly and...