They are nocturnal and tend to want to play at night, but will arouse in the day time and play and nap, and then play and nap at night too. Noisy is a subjective quality. They do not bark like a dog but the do have barks and squeeks and squeals and other noises that they use periodically. They run on wheels and if the wheel squeaks that is noisy. They tend to move furniture around and rearrange their cages. That can by noisy. They tend to chew on whatever is in the cage to chew on, including the domicile you have for them to hide in. So between chewing on it, and moving it around they can be noisy, and they do . If all of that is considered by you as noisy then they are noisy.
As for chewing on cages, they will chew on cages if the parts of the cage are wood. They will chew on anything that seems to be chewable. They chew on walls, woodwork, wall board, electric cords, books, pumice stones, branches, chew blocks, what ever is chewable. They will even nibble on you to see if you are chewable or edible. So if you make the cage out of wood, then they chew on their cages. If you let them out they chew on furniture, appliances, whatever.
The suggestion is that you have an all metal cage, a wheel, lots of chew toys (eg. wooden blocks, pumice stone, parrot toys, branches, mineral stones, etc.) to allow for chewing. Give them a house of wood, or cardboard and they will chew it too and a PVC 3-4 inch in diameter pipe joint from the hardware store (both to hide in and to chew on). I also suggest that unless you can chin-proof a room or supervise them or both, that you not let them out.
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