Right now you rightclick to lay down your basket which is not good since you rightclick really often with an empty hand in normal gameplay. It should change to shift-rightclick, just like picking it up. Accessing it could be a custom keybind or even more cool, you look up and rightclick it. Accessing it in world would just be rightclick.

It is working as intended.
Interacting with any tile entity won't place it back down. Same with placing blocks - won't trigger the shipping basket to be placed either :)