As to the other question??? What I don't know about poultry illness and injury would fill books, and does. I look to BYC's experts like
@Eggcessive above when I have questions on those subjects.
I will, however, off that you can keep your birds on that grower feed all their lives if you want, as long as they have a supplemental calcium source (like oyster shell). Your feed isn't a problem.
Anecdotally, and based on my own flock, that bird's vent looks fine.
New layers - particularly "production layer" breeds - have a high rate of "error" as they get started laying and their bodies work out any kinks in their plumbing/adjust to new nutritional and metabolic needs. According to sum sources, the rate of errors (fairy eggs, lash eggs, double yolks, etc) can average as high as 1:10 in the first couple months of lay, dropping to about 1:100 as they mature.
Nothing I've seen in your post would have me panicked. I would, however, ensure there is a supplemental calcium source available at all times.
Fortune favor you in your chicken keeping journey.