Research reward based training and dog body language. Be sure you're not using any "dominance" techniques with her as these actually show the dog that you are aggressive (staring, moving towards her, yelling, hitting, blocking, guarding, etc).

Walk time is not potty time. She should have one set potty spot where she goes every time. Take her to this spot every time it's time for her to go and wait until she goes. When you see her squat say a cue like "go potty" click your clicker and give her a treat immediately. After doing this for several weeks/months she will learn to associate go potty with eliminating. When she comes back inside if she went let her have roam of one room for 20 minutes then put her in her crate for about 20 minutes until it is time to go outside again. For this approach to work she will have to have an appropriately sized crate and be appropriately crate trained. If she is not crate trained, research it pretty extensively. This is where many dog owners go wrong.

She will try to nip and bite all of you. She is a puppy. The only thing you can do is get something like a kong that will catch her attention and keep her chewing on it for a long time to discourage innapropriate chewing. Other than that completely ignore her when she nips and walk away or if she follows you and nips and you can't get away tie her to a door until she calms down.

You will have to work on impulse control and calm behaviors to get her to stop chasing the cats. Here are a few links to some excellent videos on impulse control and calm behaviors. Basically you reward them when they are showing calm behaviors like laying down sitting or just standing and not jumping. If your puppy does not naturally calm by herself you can calm her by lowering yourself to her level and offering her calming cues. Calming cues include loud, deliberate yawning (not so loud you scare her but be audible), licking your lips, lowering your head, and looking around passively. You see dogs who are stressed do these things to calm themselves and trigger the same response in other dogs. Dogs who offer these signals during human interaction do not like the interaction and are trying to tell the human to chill out.