A rolled up poster is fairly similar to a nest hole, so I'd call that laying an egg in a nest. If she'd laid an egg out in the open somewhere we'd know that she's the type who's determined to lay eggs no matter what. Right now we can still hope that she's the type who requires a nest. But she's got one at the moment, and you need to take it away quick if you want to stop her from laying eggs. It might already be too late. The window of time between them starting to get interested in laying eggs and actually doing it is only a few days, so quick action is needed to shut them down. She could have an egg in the "pipeline" right now, or she might have already laid one.

You were right - We have 7 eggs instead of 6 today! What should I do now? Is it really bad for her to lay the third clutch?

Now about my attempt to make nights long for them. It didn't go that smooth yesterday. Normally male is sitting on eggs in the evening until they decide its time to switch for the night (when she goes to eggs). And because they were on kind of a late schedule (caused by handfeeding), they don't have this switch until about 9-ish pm. I don't remember how, but I caused him to leave the nest, thinking I would check eggs when I have a chance in the morning. Hen went in.
And normally when the male gets out of the nest, its his share time with chicks. I wrote that chicks need a parents to guide them to eat. So, instead of starting eating, he was sitting on the curtain rod, cleaning himself and preening the chicks, so relaxed. I was trying to show it was time to get into the cage and sleep but they didn't think so. Sure I can pick up all the chicks and take them to the cage (and I did) but then they would be hungry over night (which is really bad for some underweight chicks). We do have a food bowl and water in the cage but the main feeding occurs in the kitchen on a special table. Anyway, I took chicks into the cage, the hen was locked and covered in her cage (with a nest box still in). I waited when the cock eats and took him to the cage as well (which is normally not easy as he is not tame). The cage was covered at 10.05 only.

Why the handfeeding put them on the late schedule? Because I am normally busy in the evening (supper for the family, kid's classes, etc) and handfeeding was taking such a long time. I will try to do my best improving the schedule.

Any way to tell apart old eggs from the new egg?

Raising chicks puts more of a strain on the parent birds than laying eggs does. So if she has a good diet with plenty of calcium, laying eggs might not be too bad for her. It's probably too late to prevent her from laying at least one more egg, but if you take the nestbox away immediately and change the environment in other ways (like putting her in a different cage in an unfamiliar place) it might prevent her from laying a full clutch.

Candle the eggs. The new egg will not show any signs of development yet and should have a golden glow. If the old eggs were infertile they will also have a golden glow, but there may be other signs that help you tell old from new. The old eggs may have dried out a little by this time. So if 6 of the eggs have a much larger air cell than the other one, the egg with the small air cell will be the new one. If 6 eggs have a different shell color than the other one, the 'different' egg is the new one. All eggs have a slightly translucent pinkish color when they're first laid. The shell of fertile eggs will change to a stark opaque white after a few days, but I find that even infertile eggs will eventually change to this color too. I don't know whether your old eggs have done this yet or not.

it won't be easy to get parents out of the nestbox. Would you force them out?

I understand it would be useful to get rid of old eggs, but what do I do with the new egg (if I am able to tell it apart)?

So I understand I have 2 options. Force them out into the new cage with nestbox removed and hidden, or leave things as they are (with hopefully removing the old eggs)?

Yes, it's OK to force the parents out of the nestbox. You can wear a glove on your hand if you're afraid of getting bitten. Some people use a rubber spatula to chase the parents out through the door.

It's up to you to decide whether you want to take the nestbox down or let them try for another clutch. If you want to let them try again, they should go back into the nest without any problems when you allow them back in.

If you decide to take the nestbox down, save the new egg for a while and any other new eggs that the hen lays. Hopefully she will stop laying eggs in the near future; but if she keeps on laying, give the nestbox and the eggs back to her. Newly laid eggs will stay good for a week or more without being incubated, but they won't start developing until incubation begins.

I just candled the eggs. Instruction for dummies should say - shine the light underneath the egg, not just at the egg, like I did in the past . A good thing I figured this out.
They all looked about the same from outside. When candled, the egg that I think is new is having a yolk in the middle and this is it. A small yellow round in the middle, surrounded by nothing. Is it it?
I saw no fertile eggs. in all the old eggs I could see like a dividing line between the more yellow and less yellow (air sack?) , and if you move (spin) the egg, the inside is liquid so you can see it moving but the dividing line still remains between them.

While I was candling in the bathroom, I could hear the parents mating.
I will think what to do with the nestbox.

What I am concerned about is that it will be impossible to get parents into the cage for the night. last time (with the first clutch) she was sitting inside the poster hissing at me, and it was really really hard to get her out of there. When she laid the first egg, I rushed to get her a nestbox and they gladly accepted it.

When you candle, you want a narrow beam of light to pass into the egg so it lights up the inside of the egg. The traditional way to do it was to hold the egg above a candle flame (that's why it's called candling). With a small modern flashlight, you can hold the light at any angle - it can be underneath or coming from the side - but it needs to be close to the egg so the light goes into the egg and lights up the interior. If the light source is far away from the egg the light will bounce off the egg shell instead of passing through the egg.

The less yellow part of the egg is the air cell, and it sounds like you have correctly identified the old eggs and the new egg. The new egg should have an air cell too but it will be smaller than the air cell in the old eggs. If you see bubbles instead of an air cell, it means that the air cell has ruptured.

The parents will want to be where the eggs are and it would be difficult to get them away from that location. But if there is no nest and no eggs they will not have a special place where they want to be, and they might think it's desirable to be in the cage with their babies.