I wouldn't put shoes on her just because her feet are soft. She may have other issues that shoes would make worse. You really need to find out what she is being fed and by the weight, not the scoop.
If gravel makes indents on the hooves that doesn't seem to be right. You really need to post more pictures. We need to see the outside of the hoof not just the underside, also full body shots with the horse as squared up as you can get her.
Oh and Loosie I had no idea detergent soap and dish soap were two different things. I always used the terms as one in the same. So that is good to know. Is that why Dawn is used? Because it's a soap and not a detergent?