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1. Can I remove this "looks like a bag" border around a grid?
Let's do this one first:
User Settings -> Pinco's UI -> Container Settings
Uncheck "Enable Grid Legacy Containers" to get the EC default versions of the containers.
2. How can I resize a container?
When you've turned off Legacy containers and are using the EC default ones, there will be a little extra UI bit in the bottom right corner, click and drag to resize the container. Containers cannot be resized when in Legacy mode of any type. (They CAN be scaled with another feature, but this doesn't change the visible area, just zooms in/out the container)
Can I set a default container for shopping? (I buy 20 shovels and want them to be placed in a bag.)
What do "restock" and "organizer" buttons do?
These I haven't really played with, I tried the organizer feature a couple of times, but couldn't really get it to work the way I wanted it to, so I tend to leave those systems alone.