Wow, kudos to you for your hard work with Scully, which has obviously paid off - she looks so content getting her neck scratched!
Maybe she's treating the grass like it's any other prey, so it needs to be chased/batted before it's eaten? I dunno. I had a cat who'd been an outdoor cat before I adopted her, and she turned up her nose at cat toys, as if to say "I've played with the real things. These are beneath me."
Flea meds: it depends on where you live, and how warm it is. In most places (in the US at least), Nov-Feb are pretty flea-free. If you live in a cold climate, you could probably stop flea meds in Sept or Oct and not start again til spring.
I don't think there are any issues giving raw chicken as a treat, but others may have more specific info for you.
I assume she got her vaccinations as well. Again, depending on where you live, you may want to consider a rabies shot, but overall, the fewer the vaccinations, the better. Boosters are really not necessary. You can read more about that here: Vaccines for Cats: We Need to Stop Overvaccinating
However, don't worry about losing her trust if you do need to get her to a vet. I had the same fear with a stray I took care of, but after disappearing for a few hours once we got back from the vet, he came back when he was hungry. He was a little tentative about approaching for the next day or so, but that was the end of it. The next few times he had to see the vet, he resisted being confined, but once the vet visit was over, all was forgiven.
I've heard this from several other people as well. She's not likely to give up her food source, or those scratches that she likes so much!
I didn't want my stray inside either, so he had his little house in my screened-in porch, with a heating pad and cat bed in it. I let him in a few times when the weather was really awful. He liked coming in, but he got very anxious if I didn't let him back out after a few hours. A couple of years ago, a starving stray showed up, but in my case, my resident stray kept chasing her away. I tried to set up another shelter for her on my deck, and then on the other side of the house, but I guess he kept chasing her off. Every night when I went out to feed her, she was farther away, so I brought her (and her fleas) in.
If you're willing, you could try setting up a feeding station/shelter somewhere away from where Scully's area is. Maybe you'd have more success than I did, since Scully isn't chasing the new kitty away. Or you could contact a local rescue group to try to trap the new little guy (or girl).