Hello there and welcome to the forum!
As a rule, the bigger the cage the better. So your cage sounds perfect.
As for safe wood, you need to be absolutely certain on the type of wood it is before offering it to your cockatiel as some woods are highly toxic.
This website page has a list of safe and unsafe plants and below that a list of safe and toxic wood.
As a rule, the bigger the cage the better. So your cage sounds perfect.
As for safe wood, you need to be absolutely certain on the type of wood it is before offering it to your cockatiel as some woods are highly toxic.
This website page has a list of safe and unsafe plants and below that a list of safe and toxic wood.