Don't let cockatiels sit on it lol. Actually it's best to cover it up with something like a blanket or towel so they can't chew on the wood. Chewing on wood is an instinctive activity that cockatiels enjoy, and you can't train a bird to not follow its instincts. So all we can do is protect the wood from the beaks.

My cockatiels were chewing on my window frames. I taped plastic over them. They were chewing on my books. so I put a towel over the top of the books. They were trying to remove keys from my laptop so I purchased a "skin" to protect it. They like to sit on my lampshades and poop on them. I haven't found a great solution yet.

I taped a scotch tape on the window frame but they now unpeeling it and chewing on it too, which may not be safe for them at all. They even chew off pieces on the plastic window blinds (there is a hard plastic board on top that they sit on, so they are destroying it). Otherwise, open cabinet doors are their favorite, and its nearly impossible to make sure those stay close (my life is too hectic), and there is couple of towels for them there.
what kind of plastic, Dianne?

It was too soon to say parents were eating much better this time. At the day one she was trying everything and this made me think she changed. Not so much anymore. For some reasons, they almost completely ignore green veggies, even though Cuddles always liked them and ate a lot with the first clutch.
Nobody was interested to eat formula so I probably won't waste it anymore.
Otherwise, she eats a little here, a little there. Trillie eats mostly bread to feed the babies.
I mostly see older chicks eating sprouted seeds.
I today decided not to give them toasted waffles to see if they would eat more other food.

Do I have to remove door with the spring to mount the nestbox in the new cage?

I wasn't sure how to remove the spring door so instead I opened it all the way and tied it to the side of the cage in the open position. Then I attached the nest to the cage.

do chicks fall all the way down when they fledge? you probably have a perch next to the door opening, but they won't always make on it successfully.
somebody mentioned a rubber shelf they attached inside the cage - its like the second floor for the fledglings but I don't know how to implement it.

every day is the same problem. They both leave the nest around noon time. I guess Cuddles has all the rights not to be in, so its Trillie's responsibility to stay with the chicks, that he ignores. Lack of experience again. And he is not tame. I can't take him in, and I would hate to pick up Cuddles to put her in. She deserves a break.
While I was typing, Cuddles went in.

I do have a perch just outside the nestbox door, but sooner or later the chicks will fall off and go all the way down to the floor. But they instinctively flap on the way down so they don't have a hard landing. I've never had a chick get hurt from falling on the cage floor.

How long do the parents stay out of the nest? If it's only for a few minutes it's OK. If it's for a long time it might be a problem, but the babies and unhatched eggs will keep each other warm for a while. When the oldest chick is about a week old it's normal for the parents to start spending almost all their time out of the nest during the daytime.

Plastic for windows--in answer to your question.
I did this in a bit of a rush. I took some kind of clear plastic drop cloth and used double stick tape to tape it to the top of the window frames. It hangs down about 12". I did the same thing with the top of a (very expensive) wood picture frame that they were starting to chew. I did this several months ago, and they now never go to the top of the windows. I may just be lucky LOL. Before I did this they were up there a lot and I was worried about them chewing on the frames, both because of how it looked, but also because I thought it might be bad for them. The frames are made of Multi Density Fiberboard (MDF) and painted.

I think the older babies are a lot of distraction for the cock, I even had a though to take them away (downstairs, or even to the bird hotel for a few days).
Yesterday he wouldn't sit with the newborns even when I locked him in the breeding cage (nobody was crying for food at that time). Hen is being a very good mom - every time she realizes nobody in the box, she goes in. Today he does sitting a little better, but I certainly will put him into breeding cage every night (want him to realize he is in charge too).
There are still 5 chicks and 3 eggs. they are staying all together.

Diane thanks. Our furniture is old and I hope its just wood. Mostly I am talking about built-in kitchen furniture. Will need to figure out how to prevent them from chewing it (so many things to figure out...... )