When your dog is dreaming and making strange noises and shaking all over, I've often wished I could ask it what the dream was about that made them react so much, lol.
Coyotes are highly intelligent. They will send out a female from their pack to lure in a male dog and then they will pounce on it.
We live in the country and used to have coyotes roam across our acreage. Then we put up a 4' high fence all around and that stopped them for good and haven't seen a single one since. I've read though that they can get over a 4' fence so we don't rely on it as being 100%. We also have our front and rear yards fenced as an extra precaution. There's a pack of them not too far from us and sometimes when we're in the hot tub in the evening, we can hear them howling away. A neighbor near us and closer to the pack had his dog go missing (no fence) a few years ago and I'm certain it was the coyotes that got it.
Coyote poop can sometimes contain
parvovirusparvovirus. Our old black lab contracted parvo even though she had been vaccinated against it. I used to take her and our Springer for a walk around our property and she must have come in contact with coyote poop as she hadn't been off our property for the weeks prior. I was fortunate to get her into the vet quickly enough and she recovered fine. Our Springer (vaccinated also) did not get the parvo.