Trash problem: Keep the trash in a child-proof cabinet or behind a secure door in the pantry. Trash problem solved. Trash is just too darn tempting, so it's best to keep that away from any youngster.
How hard do you tank your pup back? Do you wait until she's hitting the end of the leash and barking like mad and then drag her back sharply? She's probably scared of the sudden reaction, hence why she's rolling over. Or she thinks it's a game of horseplay- it all depends on the context of her mood. Have you tried distracting her from the cats with treats or even a hearty game of tug? How much exercise is she getting? If she's 7 months old, is she enrolled in an obedience class? If not, why aren't you enrolling her in one NOW? You both need to go to obedience classes where you can learn how to teach and train her, she can learn how to operate under distractions and drain energy, and you both can have a slightly calmer life.
She sounds like a normal puppy. Yes, you do need to provide strong leadership and yes you need to control her environment. Put the cats up in a cat-safe room when things are getting too heated between cats and dog or crate your dog for a settle-down period with a nice, stuffed and frozen kong to work on. Go to obedience classes to further leadership, training, and good behavior. Keep the leash up and away so she cannot chew on it and when she has it on, watch her carefully so that she doesn't mouth it! If she does, correct her and then stuff a good chew toy in her mouth. If she keeps going for the leash, be the more stubborn one and keep shoving that toy in her mouth! Engage her in a game with the toy! The leash is boooooring, the toy is fun fun fun!
She just needs more exercise, training, stimulation, and good leadership. Normal young adolescent.