Yeah, that looks normal for molting! Those are, indeed, her new feathers coming in that you're seeing.
As for why she's molting again, it's hard to say. I have had hens molt very early in the year and then not molt in the fall. One likes to molt multiple times in the year, seemingly at random. My birds who go broody tend to molt immediately afterwards as well. Did she try to hatch eggs recently?
It could also have to do with the lighting she's under. Do you keep her under completely natural lighting? Sometimes electric lighting? The hormones that trigger molt are heavily influenced by the length of daylight that a bird is exposed to, so any additional lighting from the normal day length could trigger a molt. She could also have been triggered if she's in a darker area of your home without much lighting.
I don't think you have anything to worry about regarding her health as long as she's on a balanced feed with a good protein level. I'm not sure what's available in your country, but if she's been doing well and gone through molts already on the feed she's on, she should be fine!