Conure laid egg on cage floor, parents protective. What should I do?

It's possible. If she's ready to lay eggs and has already started, the nest box and moving the egg to it may encourage her to finish laying there and to stay on them. First time mothers can also sometimes not sit on the eggs properly or be competent in raising young so if you think the egg is viable and she refuses to lay on it, you may need to attempt to incubate it yourself and hand-rear any that hatch.

Leave them in the nest or nest box for a couple weeks, then remove one egg each week until they are gone. Removing them too soon or all at once may trigger more egg laying. You can also lower room temperature by a few degrees and limit her exposure to light. Shorten her days by using a cage cover in the early evening.

A female does not need a male in order to lay eggs. Once she matures (at around 1 year old), she will begin to lay eggs. They will be infertile in the absence of a male. If placed together and conditions are right, they may mate and she will lay fertile eggs. They typically lay a clutch of 4-6 eggs with 24-48 hours between eggs. Incubation lasts about 3-4 weeks.

She will lay eggs with or without a male present. Provide a suitable nesting box to keep the eggs secure. Any eggs she lays in the next few days may be fertile. Most birds lay one egg every 24 hours until a clutch of 4-6 eggs is in the nest, then incubation will begin.

If you are hoping to raise babies, then providing nesting material for the parents is best so that they can make a safe nest where the eggs are less likely to fall or break. The parents may also break eggs or discard them if they aren't viable or they are young parents that don't know what to do. Because the eggs need to be incubated, they need to remain in the nest with the parents in order to hatch. You can keep letting both parents try to raise a clutch (and be sure to provide a calcium supplement for the mother), or, if you don't wish to raise babies, can just remove and discard any laid eggs.

It's very hard to tell, she would need to be taken to an avian vet specialist to get calcium injections, SC fluids and also have an xray done to make sure no damage has been done and that no more eggs are inside her.

You can remove it or leave it in there for a few days. Some birds may be broody at first and she may not want you to take the egg. It won’t hurt her to lay in it for a couple days. All female birds will lay eggs even if there is not a male present. These eggs are not fertilized so throwing them away is fine. I hope this is helpful and please feel free to post any additional questions.