What a gorgeous girl! And kudos to you for taking her in.
Did the previous owner give you any insights about her personality, or behavior quirks? Does she like petting, being picked up, is she more independent, or a lap cat, etc.? Even if she is a velcro kitty, she's scared right now. It is totally normal for cats to hide when in unfamiliar places. Some cats won't hide at all, others may hide for days, or even a few weeks, before they are convinced that things are ok and that the new humans are not scary.
You're doing absolutely the right thing by just sitting with her and putting her food, water, and litter close by. She will probably eat, drink, and do her business when you're sleeping. As tempting as it is, don't try to touch her or pet her. She doesn't know you yet and may sense that you're not completely comfortable with her either, so you both need time to learn about each other. I will tell you that you will need to adjust your behavior to suit her needs; it ain't gonna happen the other way around.
If you don't force things, she'll eventually come out on her own. But even then, wait for her to make first contact before trying to touch her, or you might send her right under the bed again. She might swish around your legs, give you a head butt, or you may just find her in your lap one day. That happens.
I had a very skittish cat who, even after 16 years with me, would flinch if I approached her with my palm down, so I learned to reach towards her gently, always with my palm up, and let her sniff my hand (yes, the same one I'd had all 16 years) thoroughly before I pet her. That might be a good approach when Ava gives you the green light.
Also, I'd provide a couple of other safe spots. You can make a little bed with a towel, or get a cat bed, and put it in a quiet place, preferably high up. Maybe one in a corner of the closet, one on a chair or the top of a bookcase, etc. A cat tree is another thing that most cats really like. They can survey their domain from the top level.
A pheromone diffuser, like Comfort Zone, works really well to help kitty anxiety. It doesn't smell like anything to humans, but it smells like cat pheromones to cats, and that can be soothing.
The scratching: cats don't do this because they're mean. Ava is telling you that she's afraid and she's making a pre-emptive strike against a perceived threat. For the time being, when you sit with her, ignore her. Pretend she's not there and do your own thing. Read a book, watch TV, whatever. Right now, she's hypervigilant and watching out in case you try to invade her safe space, so she'll relax when she sees that you're not showing any interest in her.
As for the litter, it seems like you do have non-clumping litter. She should be covering her pee, so you don't need to do anything except scoop poop and change the litter when it looks like there's no more room for her to pee or poop comfortably. I think most people use clumping litter, because scooping out pee clumps is better odor control, and it's cleaner (to me, anyway). If you change litters, do it gradually, by mixing some of the new into the old. Some cats are fussy and have preferences.
LOL, love the description of the facial depression in the dry food! Yes, just keep her on what she's used to right now so that there aren't too many changes. New food can upset their tummies, and no one likes cleaning up afterwards...
Your instincts about what to do and how to take care of her are all right on target, so I think things are going to work out really well. It just takes patience at first, but she is lucky to have someone who wants to learn how to best take care of her!