I would decide where I want the cage to be and put it there and leave it there as birds like their home to stay put. As for the rattan toy, the one that is some sort of sticks, are you certain that she is eating it or is she just tearing it into tiny pieces? They don't usually eat such things but sometimes it looks like they are until you watch them closely. Normally the only time that I have seen one actually eat the wood was if the manufacturer has flavored it and you can soak the item for a couple of hours and remove most of the flavoring as well as a lot of the color if the item is wood.
I do think that getting a second budgie is a good idea, as I said before parrots are all very highly social and in the wild they are never alone from the time they hatch until they die. They have evolved over the centuries to be with other of their kind.





