Hi

Welcome To BYC
Where did she come from?
Do you already have chicks or chickens?
Can you tell us more about her breathing issues - coughing, sneezing, any mucous/discharge from the eyes/nostrils?
First of all, she's a cute chick

Second of all, it would be a very good idea to keep her quarantined and make sure you follow some bio-security measures if you have other chickens.
Feed her chick starter or an all flock/flock raiser formula feed and provide her with extra poultry vitamins a few times a week (like Poultry Nutri-Drench). If you want to give her treats, offer a little chopped egg or a
small amount fruit or veggies, but make sure she has a source of grit (crushed granite).
Hopefully the diahhrea will resolve itself when she starts to get proper nutrition and gets treated for mites.
Since she has an infestation of mites, treat her with a Permethrin based poultry dust or spray - since she has respiratory issues, a spray would probably be best, this way you could soak a cotton ball or qtip and "dab" or target the areas that need treating (around the vent, under the wings, back, neck, etc.). DE, imho is fine for dust bathing area and use in nesting boxes, etc. as a
preventative but it is not that effective once there is an infestation.
Keep us posted.
Here's some info on quarantine and bio-security:
http://www.the-chicken-chick.com/2016/08/biosecurity-for-backyard-chickens.html
http://www.the-chicken-chick.com/2012/12/quarantine-of-backyard-chickens-why-and.html
Permethrin based treatments:
https://www.backyardchickens.com/t/1151513/pesticides-approved-for-poultry