scratch feed is fine to give her, as long as she has access to some fine grit too (feed her outside, she'll take what she wants). chick starter too.
the pasty butt thing, yes does look like that. sometimes much worse.
and soaking in warm-hot water will help it loosen but it takes time, maybe 15-20 minutes, done a couple times over the day. if you have a thermometer that can get wet, run the hot water to soak her in. if it's less than 90 degrees then it's going to feel cold to her. but you don't want over 100 probably.. remember, a birds body temp is about 103-104ish, so what's warm to you might be cold to her.
and i might suggest put her into whatever you're filling to soak, and maybe run the water in while she's standing there. so she can get used to it more gradually than just plunking her in it all at once. also, i think i would put some soap right on the pasty areas, just before putting the water in. use a liquid soap. hand soap, dish soap, or even baby shampoo. the soap will stick to it well if it's dry first, then as you add the water the soap will help soften up everything and wash away clean.
if you do have a kitchen sprayer (or even a hand-held shower sprayer would work) that would be even better. don't spray on it hard, but just a gentle stream of warm water to move the gunk off as it softens. but i would still use soap too (again a liquid soap, don't need to be scrubbing the area). and tell hubby you're using the kitchen sink. don't ask.
it can be cleaned again when you're done. chicken dirt does NOT permanently contaminate anything that soap and water can clean.
i've had all manner of critters in my kitchen sink at one time or another over my lifetime, and the sink is still there.