Is my puppy normal or do I need to hire more training to help us?

First time puppy owner here. Throwaway account because I just lurk on Reddit mainly.

I have some sort of mini poodle mix I adopted. Gemini was three months when I got her and is a little more than five months now. From the start, her anxiety was a source of anxiety for me because I just want her to have a good life. Puppy class was a wake up call.

I started doing several 10 - 15 minute walks outside most days. Sometimes on trails that are easy for her, sometimes that are a little more difficult but not anywhere near max difficulty. We also visit a dog-friendly store (10 minutes MAX and we leave if she's struggling) three or four times a week. Sometimes my neighbor lets me take along her older, chill dog and that seems to have helped a little. Gemini graduated puppy kindergarten and the trainer said Gemini made a lot of improvement in just a couple weeks.

Aside from the puppy class, I’m going to take her to obedience 101 in mid-March.

All that out of the way, I have a list of stuff I’m dealing with when out and about and was wondering if this was normal puppy stuff that will go away if I keep doing what I’m doing, or if I need to hire more help. I'm trying to train a neutral dog. It's okay if she's not social as long as she's not aggressive.

1. She often plants her feet and won’t move while walking on the leash, regardless of what's going on around her or where we are. I end up practically dragging her, making ridiculous happy noises and waving a treat at her so she doesn’t think I hate her. If I wait her out, we’ll be in that exact spot for a minimum of 15 minutes.
2. Sometimes Gemini will move along after planting her feet, other times I have to pick her up, move her a few feet, then put her down to try again. Other times she walks loose leash or barrels ahead at top speed.
3. Outside, we often still have to stand to the side while people or other dogs pass. I give her a treat as they approach, and then another after they pass and am slowly beginning to only give a treat only after they pass. She gets soft praise throughout the entire process if she’s calm. Other times I can lure her to walk past with a treat.
4. Once people/dogs pass, Gemini tries to pull after them.
5. Sometimes she gives a little woof at larger dogs, though we’ve been working on that by watching people walk their big dogs from ever decreasing distances.
6. In stores, she’ll sometimes give the same little woof at people. We take a few steps back until she doesn’t seem so alarmed and I feed her treats. Sometimes we creep a little closer but not more than maybe half a foot if only out of courtesy to the other person.
7. And then sometimes, she can pass by a person or (calm) dog as if she’s been doing it for years! Especially in stores. People can pass within half a foot of us and Gemini’s only concern is not getting stepped on.
8. She peed herself when she heard a big flag flapping in the wind.
9. We got past scooters and bicycles pretty well, still working on cars, but Gemini lost her mind today watching two guys skateboard down a hill. That was the first time I ever heard her give a real bark. She did better the second time we saw them, but was clearly not happy with the arrangement and would only take the highest of high value treats.
10. Sometimes she’s afraid of weird sounds like bouncing basketballs, other times she wants to approach. I let her get within a few feet, treating and softly praising the entire time. But then the next day she’s scared again!
11. Sometimes she'll let strange people give her a treat and a little scratch under the chin, but that's it. And then other times she backs away until she's by my feet and I explain that she's scared and wants space.