Having a few issues with my new puppy- help needed and well appreciated.

I rescued a Labrador/Australian cattle dog mix from a family who had her locked in a small crate in an overly hot house. She also hadn’t been fed for at least two days before I rescued her. I’m under the impression this is where her problems stemmed from. She’s about 4 months old and very very aggressive when it comes to food. If she sees food she will try to run. No- sprint, towards it. I would put food in the other dogs (we have 4 in total now) bowls and she would run after it. If she sees another dog eating she will practically attack them to take their food. (I’ve started separating her when she eats but one of my dogs eats irregularly so we have to leave his food down but they will go after each other if she tries eating it. The other so is a chihuahua though but very “tough”) She is also very protective over toys. If another dog has her toy she will also go after them to get the toy. Not playfully either. I’m not sure why she’s so aggressive but my family and I think she may have had to compete for food in the past. She also get separation anxiety or something. She will cry and bark when left alone in a room or crate. These are the few main issues. She is also very nippy and I’m not sure how to handle the biting but in trying different methods like rolling her over and holding her gently by the scruff of her neck until she calms down and doesn’t bite. I’m not sure if this is inhumane or not. I’m under the impression it’s okay. I’ve also tried over exaggerating pain and making crying noises to try to discourage it because I don’t know what to do really. Other than that she’s calm and a pretty cuddly little pup. Any ideas for any of these issues is well appreciated

Edit- I’m not sure if this will help with any ideas or understanding but she also likes to be around me all the time. I just got her a few days and she’s almost always in the same room as me. If not I can guarantee to see her within 2 minutes of her discovering I’m not there. She even sits at the bottom of the stairs until she’s sure I’m coming with her.

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from Pets https://www.reddit.com/r/Pets/comments/cgmdom/having_a_few_issues_with_my_new_puppy_help_needed/