Will these eggs hatch? Should I take the eggs away and throw them out and try to have her start again.
Hard to answer. I don’t give a broody any eggs to hatch until she proves to me that she is serious about being broody. That means she has to spend two consecutive nights on the nest. I’ve had them tease me about being broody before.
During hot weather, I’ve seen broodies spend an hour or more at a time off the nest. Those eggs hatched fine. During cooler weather, broodies spend a lot less time off the nest. There are no specific rules about time on or off the nest they have to follow. I don’t know how much time she spent in or off the nest or how cool it is where you are.
Can I put eggs from other chickens underneath her?
You certainly can. You can put turkey or guinea eggs under her if you want to. She’ll hatch them. They cannot tell which eggs they laid.
Should I lock her in the cage and just feed and water her in there?
Hens have been hatching eggs with the flock for thousands of years, so you don’t have to. However, a lot of people do isolate the broody. There is no right or wrong about this since we all have different conditions and circumstances. If you leave her with the flock, mark the eggs you want her to hatch and check under her daily to remove any new eggs that might show up. The risk if you move her is that she might break from being broody. But people move them all the time.
There is a whole lot I don’t know about your goals or circumstances which makes it hard to give solid advice. If it were me, I’d probably leave a few marked eggs under her so she remains broody, while gathering the eggs I want her to hatch. When I had all the eggs I wanted her to hatch, I’d mark them, remove the decoy eggs and trashy them, and put the “good” eggs under her. I suggest this just so you know what you are dealing with and you know they all started at the same time. It sounds like you are uncertain about exactly what has gone on with the eggs she is on now. It would be a shame to go through the process when you are not pretty sure she will be able to hatch. But I won’t criticize you if you decide to go forward with the eggs she has. I think there is a real good chance some or most will hatch.
In my opinion, in any of this, there is no right or wrong answer that covers all of us. It’s just the way you decide to go forward. There are a lot of people on this forum that do things differently than I do them.