Some interesting eggshell colors in that nest. I don't think they were all laid by the same hen.
The float test doesn't really tell you if the eggs are good or bad. It gives you an idea of how old they are. The longer an egg is stored the more moisture it loses.. After a while the air cell gets big enough that the egg will stand up on the bottom with the air cell up. When it loses more moisture it actually floats. The test is to fill a bowl or basin with water and put an egg in there. If it floats it is older. If it sinks it is fresher.
About the last part of a hen laying an egg is when she puts a coat we call "bloom" on it. It's a liquid so the egg looks wet when it comes out but it quickly dries. That layer of bloom is really good about keeping bacteria out of the porous shell. If bacteria gets inside, they multiply and causes the egg to be rotten. That's where the rotten egg smell comes from. Bloom is so effective a hen can lay eggs in a hidden nest until she gets a brood and then incubate them for another three weeks before they hatch without bacteria getting inside. Turkey and duck eggs can go longer. If the bloom is compromised bacteria can get inside so a rotten egg is possible, but you should be able to smell that through the porous shell.
You can certainly toss any of them that float if you wish or just toss all of them and don't worry about them. Lots of people do either. Did you know that when you boil a fresh egg they can be hard to peel while an older egg usually peels really well?