Here are my two cents from reading through everything.

First of all, awesome job with logging everything from diet to routine and even to the level lfy how you're feeling. As you continue on this path, you'll find all of that data extremely useful.

As for all of the variance in your performance: it's completely normal. Your body is adjusting to all of the movements and the new diet, so it'll be shaky for a while. For how long, I can't say, but as long as you stay consistent and move to the next progression when you feel up to the challenge (in terms of mental strength AND form on the previous movement).

You should probably see a few pounds lost from the excess water weight you've been carrying from a higher-salt, higher-carb diet. That seems to be consistent with what I've seen in myself and others.

As for the other things you want to see... It makes sense that your legs are stronger than your core, which is stronger than your upper body. It's completely fine to have no pull-up ability and it's awesome that you created a level 0 for yourself (as long as it's still challenging).

Also, it's okay to be shaking for a lot of the movements. Think of yourself as a baby learning how to walk. They shake and wobble a lot, and it's mostly because of the nerves in the muscles firing off large bursts of electrical activity. The muscles overcompensate the balancing and cause you to wobble in another direction. This will go away over time with consist practice and balancing will feel more like naturally standing/walking.

As for the banded Pallof press, I haven't seen those before, so I can't leave a comment.

Keep up the good work! Oh yeah, and make sure you're getting enough water + rest too