All I can say is that she's a puppy and with this one there might be more drive so training will take longer. You said after 2 months...so I'm assuming she's around 4 months old...so I wouldn't expect that much from her. Maybe you are comparing her to your last dog too much and not realizing that your last dog wasn't a perfect citizen after 4 months either.
Not all training techniques work with all dogs. Maybe positive only won't work with this one. She might have more drive and be more hard headed, and your positive only outlook will only teach her to be more independent (if she truly doesn't care about your approval). The "ipping" technique doesn't work with all dogs either. Some dogs don't care if they're hurting the other dog (what the ipping simulates) and won't stop. If she did come from a questionable breeder, and was taken away at 6 weeks, she might not have learned good enough manners from her litter in order to associate the "ip" with a dog in pain.
Stick with it, and don't expect too much. She's a puppy, have fun with her, don't expect her to be an obedience robot from day one.
The only thing that's alarming is her unpredictability around new people. That might be a poor genetics type thing. At this age, she should be very happy to meet anything and everything. They shouldn't cower, hide, and they shouldn't snap and lunge either. Out of all the things you've written, that is the only one that is truly alarming IMO. That will take more training, more controlled socialization, and has the chance to grow into a bigger problem. It might also be signs of a 4 month old fear stage which many dogs go through. There are many ways to look at it.
CD RE TC HIC 7/10