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Unfortunately, your photos did not come through, and you do not mention how much light they receive.

Usually, this is caused by lack of light, though.

https://www.gardeningknowhow.com/garden-how-to/propagation/seeds/leggy-seedling.htm

I use a chopstick, or wait until each single seedling fills out its single cell, completely with roots. If you have them planted together, instead of each to a single cell, then you will need to use a chopstick and catch them before their roots tangle.

If you plant one seed per cell, then you will wait until it fills that cell with roots. Then it will pull out in one piece.

https://www.gardeningknowhow.com/garden-how-to/propagation/seeds/seedlings-after-germination.htm

Wow, you've done a great job! The ones that are stretching do need more light, either the LED or a sunny window. They need six hours of full sun. I would let them start to dry between waterings. You can move them up in pot size if they seem to be outgrowing the small pots.

We have info on this website for each of those veggies: http://www.gardeningknowhow.com

https://www.gardeningknowhow.com/edible/vegetables/vgen/growing-vegetables-with-seeds.htm

Are you saying the roots are out of the soil? If so, use a small tool like a fork or knife and try to replant them, disrupting the root as little as possible.

If the roots are still below the soil the seedlings should be OK.

https://www.gardeningknowhow.com/garden-how-to/propagation/seeds/seed-starting-mistakes.htm

https://www.gardeningknowhow.com/garden-how-to/propagation/seeds/what-is-damping-off.htm

https://www.gardeningknowhow.com/garden-how-to/propagation/seeds

You could choose, either, containers for them or they can grow out in a prepared patch. The corn won't be too hard to transplant If you go with a container, then make sure it is at least a foot deep and a foot wide. You can grow those two, and add beans or peas with them. Both are beneficial to corn and the corn is beneficial to them. Corn offers support for the beans and peas, while the beans and peas feed the corn by harnessing nitrogen from the air. For in ground planting, the depth doesn't matter. Just plant with beans and peas, either way.

The cosmos is a little trickier. I would advise container life for the first plant set. Once you get some seeds, you will direct sow in the place that you want them. Each one will need to be carefully removed by spooning out under them. Slowly pull them apart and slowly transplant them a few inches apart in your container. They are simple to grow, so not much care is needed. These articles will help:

https://www.gardeningknowhow.com/garden-how-to/propagation/seeds/seedlings-after-germination.htm

https://www.gardeningknowhow.com/edible/vegetables/corn/corn-seedlings-with-blight.htm

https://www.gardeningknowhow.com/ornamental/flowers/cosmos/growing-cosmos.htm

This damping off happens most often when it is too moist. Seedlings need just a little time to dry out on the surface between waterings. I would try again using brand new soil just in case there is a disease from wet soils.

https://www.gardeningknowhow.com/garden-how-to/propagation/seeds/seedlings-after-germination.htm