No idea where they came from though.
Turkeys can fly perfectly well, so they could have come from anywhere.
Rats are amazing. I've had a lot as pets, but my favourite was one that we raised from a newborn. She was super friendly and had no fear. At one point she figured out how to escape the cage, did it three times before we fixed the cage so she couldn't. Each time she escaped in the dead of night, and apparently wandered the house until she found an occupied bed and then climbed up to visit the sleeping human. Three different times, three different beds. Family members weren't impressed.
My parents had a rat that got out pretty consistently. But it never seemed comfortably away from the safety of it's cage, and it would only crawl up to the top (it was a three story cage, nearly as tall as me), and sit up there for a few hours every now and again. My mom would dutifully put him back in, but when she didn't he'd find his way back in on his own. This went on for about a month and a half.
I finally stayed up for a few hours one night watching it to figure out how it was getting out - one of the welds on the metal bars in a lower corner had come loose, and though visually it looked indistinguishable, the rat was able to push it to the side and scale the cage. It had a bit more difficulty getting back in - it seemed to remember the general area but not the specific bar. We were worried the dog was going to get it one of these days (the rats tormented and taunted the dog constantly) so we made sure to seal it up again.