The limitation on making better batteries is research, having a NA factory isn't going to help that. As per increasing the rate and reducing the cost, I don't have a good answer for that, Li-Ion battery production is already incredibly automated I'm not sure how much they can improve the rates. I would be surprised if Tesla hasn't figured out the supply chain management for all the materials they require.

I'm still sort of skeptical about this factory. There have been very few battery manufacturing plants ever built in North America over the years and they have pretty much all shut down (A123, E-One Moli, and Delphi are the three that come to mind) as they don't make money.