Cockatiels can eat honey. They love honey. It may surprise you, but honey is used in many cockatiel treats (to hold seeds together). So, yes, cockatiels are allowed to eat honey - in moderation, though!
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Yes, cockatiels can eat corn. Not that they will like it, and it may take them a while to get used to it if it is a major change in their diet but corn will not hurt a cockatiel.
Yes, cockatiels can eat bread. However, they should be supplied with plenty of fresh water at the same time, to balance the dryness of the bread.
Cockatiels can eat celery, however, it has no nutritional value - it is mainly water. Don't give your cockatiel too much, everything has to be eaten in moderation.