I need some help...

You already know several things about her....she has low confidence; and, she is both sight and sound reactive. Your training should start with building the confidence level first and then tackle either the sight or the sound reactiveness but, not both at the same time.
She's in a new environment and as you've noted, her confidence level is coming up so, you're on the right track. Routine and structure alone have a great calming effect on dogs...they just need a little time to put everything in order. That's your task.....showing her what she needs to do....ie: Sit for food/petting, Down when the doorbell rings, etc.....set the rules and make them clear. She's still trying to sort out what she's supposed to do when/how and why...ease her mind....that gives her confidence in knowing how to handle the simple things.
For the reactiveness, I would work on sight first as it's not usually as intense as sound. Get her used to seeing strange objects in the room. Open an umbrella and put it on the floor when she's out of the room. Let her approach it on her own. Praise and treat for showing curiosity/confidence to approach the umbrella but, don't make a huge deal of it. Use other strange objects but, stay away from things that hang from the ceiling for the time being....she's probably not ready for that.
Practice walking in the house....bonding and building trust with you. Praise and treat WHILE SHE IS WALKING...don't stop to treat. Getting her to focus on you, looking to you for guidance instead of focusing on other things will certainly help on your walks. Then you practice on the back deck, then the backyard. When you think she's ready you go down the street a little ways and then back. Build the distance slowly while you continue to work on the other training because the further you get from home, the more nervous she'll be.

Yes, wait on the umbrella. Confidence building is a slow, detailed process. It starts out by having trust in you as the leader and you did exactly the right thing by tossing treats. That's the very first step...tossing treats...showing her that really good things come from you. Initially, she doesn't have to earn/work for all of them....that's not the goal at this stage.
When you toss treats, she starts to pay more attention to you....a very good thing! Next stage is that she starts to move closer to you (has some trust/confidence in you) ON HER OWN without you enticing her. Next comes following you around...more confidence in you. Here's where you start upping the ante...will she follow you (confidently) through a narrow opening....doorways/narrow places are scary for puppies. That's why going outside (through a door) is sometimes tricky...it's partly the door and it also opens out to some scary sights/sounds.
When she is following you happilly into every room of the house and has investigated every nook and corner is when you can introduce something new to the room.
When you're outside, toss treats into the grass...use really good treats...SPAM, liver, cheese, etc. Walk around....talk softly to her....she should have the confidence to venture into the scary world as long as you are by her side...it may be tenative but, reward/praise for following you around.

When dogs play they practice all the life skills....dominance/submission, takedowns, 'kills', bluff/bluster, on top/then on bottom, chaser/chasee and sex.
Forget the dominance thing. One dog might hoard toys, while the other might hoard the best sleeping spot(s) so, it's foolish to say one is being more dominant than the other. You will find dogs are 'dominant' about some things but 'submissive' about others.
Typical of any family, there will be minor squabbles from time to time but, they will work it out. The point where you step in is if you see signs of bullying behavior (trying to keep the other dog out of a room, not letting the other dog back into the house, away from a person, charging across the room and pouncing on the other dog/not play) or the squabble doesn't look like it's going to end quickly....you want to stop it before it escalates.
Dogs play rough and they are usually quite vocal....snarls, barks, woofs, yips and teeth are all part of the game. Truly aggressive dogs seldom issue warnings with either barks or growls. There are no playbows and no invitations are given. They just attack with the intent to kill or maim.