Cesar Millan says, "We don't get the dog we want; we get the dog we need." Indeed! I had a similar experience with my Bo. He's the exact opposite of Bea in every way possible!
Problem #1 is very easy to solve. Practice "no touch, no talk, no eye contact" whenever you're taking her anywhere. Your parents --- and everyone else in the house -- need to ignore the dog completely and wait until SHE APPROACHES THE HUMAN. What happens when you bring her in the house right? Everyone's like "OMG LOOK AT THE PUPPY" and freaking out. Ignore her. Explain to strangers wherever you go that your pup is in training for anxiety issues --- people will understand. Dogs will seek out companionship - its in their DNA to be part of a pack. And when she does, don't make a huge production out of it - just love her; good, positive energy only at first. All the attention is overwhelming her right now. She needs to find her own way in her own time. And she will!!!
#2 Part of what you describe sounds like what Bo does anytime anyone LOOKS at Bea. HE wants all the whatever-it-is she is getting; pets, cookies, attention, whatever. Bo is trying to manipulate the situation. I simply disagree with this behavior (so he knows what I don't like) and put a stop to his efforts by moving him away from where the "action" is via his leash or a sit / stay (which he NEVER stay in by the way LOL) Hey, we're a work in progress! LOL As for that sudden burst of energy; embrace it! I think "crazy dog" is fun!
#3 She's too young to have free roam in the house. That mountain rock eating could turn into an electrical cord and you'll have a dead dog when you get home.
Crate or exercise pen your pups when you cannot watch them. Put a puppy gate up in a "safe" room or something.
#4 Practice leadership on your walks. That grabbing them from the neck is NOT a good thing. You control the meeting when you encounter other dogs. If she's being dominant, turn her around and hold her butt so she's offering her scent to the new dog. I had to do this with Bo yesterday...not because of Bo but because the other dog (a friend's new rescue Puggle) was all hackles up, being defensive. Bo wouldn't have done anything --- I know that -- so it helped put the Puggle at ease at first and then they were fine. Bo is pretty balanced most of the time so I trust him in dog meetings. Bea is the one that can get snippity so I have to introduce them to new dogs one at a time; Bo first. Practice will make perfect -- with time -- and eventually, I won't have to do that.
Congrats on your new pack member!! I can't believe I ever had just one dog. Two is fabulous....three or four? Oh WHAT A DREAM THAT WOULD BE! LOL No, I'm not looking to add to my pack. I'm good with what I have.......