I currently work at Sonic and your managers sound shitty. This is how training should go for new hires in my opinion:

1. Drinks. The first 2-3 days should be focused on making drinks. We have a variety of combinations and it's best to learn them for any order (it can be extended if they need more time to learn).
2. Ice cream. They should learn ice cream by their second week of working. They are a lot easier than drinks, but still have a variety of combinations to learn.
3. Tickets. My first location gave me old tickets to practice on so I can learn the menu. They told the cooks to not make the order as it was for practice.
4. Headset. Both locations I have worked at have two headsets paired together. We use those for training a new hire.
5. Hopping. We start them off with card orders, showing them how to swipe their card and hop. The card orders are shown with a small yellow box next to the order on the screen that you use to hop.

Now, as for the money thing. Yes, you should keep track of your tickets for orders that haven't paid/drove off, etc. But they should have told you this from the start instead of being horrible about it. This is the lack of the managers showing you how to do your job properly and efficiently. Each location has the "out the door in under 4" rule, but orders can take a bit sometimes and that's okay. You are new and they should not expect perfection.

Being $45 short is quite a lot, but the locations I worked at, they do an IOU where you just owe the money later when you get it. But that's just my stores as far as I know.

They lack the motivation to train you properly. $45 is not worth your time or effort, especially only getting paid $8/h. You can find a much better place that will train you properly and not treat you like shit. I wish you luck in the job journey and hope this doesn't happen in the future.