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Usually not, unless they are left sitting in water for too long. Allow them to dry out some. Too much could lead to damping off. Here is more information on that: https://www.gardeningknowhow.com/garden-how-to/seeds/what-is-damping-off.htm

Actually, you can but most people prefer to do closer plantings to allow for those that do not germinate. Thinning simply helps you keep the strongest of the plants while cutting out the less robust plants.

No, you don't have to do this. Once they reach a healthy enough size, you can simply transplant them straight to the garden, though hardening them off first is recommended. These articles should help:https://www.gardeningknowhow.com/garden-how-to/seeds/when-to-transplant-a-seedling-plant-into-the-garden.htm, https://www.gardeningknowhow.com/garden-how-to/seeds/how-to-harden-off-your-seedlings.htm

You actually do not want to fertilize seedlings until they have 1 or 2 sets of true leaves, as the fertilizer can burn the new roots. After they get some true leaves, you can fertilize at half strength with a balanced fertilizer once and that should be enough for them until they are planted out.

These articles will help: https://www.gardeningknowhow.com/garden-how-to/seeds/how-to-harden-off-your-seedlings.htm, https://www.gardeningknowhow.com/garden-how-to/seeds/when-to-transplant-a-seedling-plant-into-the-garden.htm

No. It should be ok for them to remain in those pots for another 2 weeks, provided they do not overgrow them or become rootbound before then (which they sohuldn't).