They could survive in your house. While Fowl Mites will not live on you, they can bite you and cause irritation.
This post can help you with Mites in the house as well as on your birds.
https://www.backyardchickens.com/threads/mite-infestation-starting-new-post.1630760/post-27847239
The Mites are on her and would also be in the housing/coop, so likely your other hens may have them too. It's a must to rid the housing/coop of Mites since they do infest the coop as well as the birds.
For birds, I too like to use a Permethrin based poultry dust to dust each bird. I put the dust in a sock, then use it like a powder puff to dust all over, working the dust all the way through the feathers to the skin. Make sure to get around the vent, under wings, etc. Since your one hen is infested, do be sure to get her head and neck too, as you dust, the Mites will move to areas not covered.
For Housing, I like to use Permethrin concentrate (Permethrin 10) it's economical and can be mixed in a spray bottle or larger sprayer to cover larger areas. Spray nooks/crannies, nesting boxes, roosting bars, etc. Clean out bedding and throw away or burn it, don't compost it.
Repeat treating housing in 5day intervals to help break the cycle. It seems like you may have to repeat and work on Mites for a while unfortunately.
For this hen that is infested, hopefully you can get rid of the Mites on her. Mites often infest weaker birds and can bring them down even more. See that she's drinking and eating. I'd also direct dose her with poultry vitamins a few times a week to see if that helps bring her up some.
I spent the evening bleaching and spraying alcohol all over my basement utility room. Washed and dried (hot setting) all my clothes and showered twice. My basement will be off limits to my cat for the next month until any I missed die off due to starvation.
