Thank you so much for sharing your story with us! I'm so touched and so happy for you guys to have adopted your sweet Yorkie! It's so nice to hear how she slowly warmed up to you. It makes me smile to read how patient you are with her to make sure she feels safe and comfortable! It's just so wonderful...
As for her getting over her fears...
Do you have a clicker? Does she have certain treats she's okay to eat without getting an upset stomach? I would suggest doing some daily positive conditioning on her with all the things/sounds she fears.
For example, with the closed door situation:
- Sit with her with the door open - if quiet, click and treat
- then door halfway closed - if quiet, click and treat
- then door slightly ajar - if quiet, click and treat
- close the door - if quiet, click and treat
She might get nervous once you have the door almost closed. That means it's too much, so open it back up a little and click 'n treat. You could either say comforting things to her, pet her, do something that comforts her, or just sit in silence during this training. The point is to associate good things with the door opened or closed. Once she's okay with the door closed for a few seconds, quickly open it again and click 'n treat. Then close again for longer, open the door again, and click 'n treat. Until she can sit with the door closed for a few minutes, then click 'n treat with the door closed. You get the picture

You might have to do this over a span of many days or a couple weeks.
Very important: make sure you don't click or treat if she barks - this will reinforce her to bark. If she barks, stay calm, open the door back and wait until she's calm and quiet again.
You can also use this gradual conditioning technique to everything else she fears, even noises.
You can read more on clicker training here (it's
amazing how much dogs can learn this way!):
What Is Clicker Training? | Karen Pryor Clicker Training
It takes a lot of time and patience to get over fears. But I think you got the loving, caring, patience thing down already! You might learn that she's actually really smart! She might get over her fears quicker than you expected and you can move on to training her tricks using the clicker too