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They are normally started indoors about 4-6 weeks before the last frost in your area.

Most seeds require warm temperatures to germinate, usually at least 55-60 degree F., depending on the plant being grown. While 40 degree temps will not likely hurt the seedlings (as they're protected), it could inhibit the germination of the other seed plants.

I personally use fluorescent shop lights for starting seeds indoors. They are cheaper and work just as well as the more expensive grow lights. You can buy them for about $8 each at the hardware store, including the bulbs. Plain fluorescent bulbs will work just fine.

The rule of thumb is that you can transplant them when they have 2 sets of true leaves. True leaves are the leaves that normally appear on the plant, not the leaves that appear when they are first sprouting. With some plants with small seeds, like snapdragons for example, it is not uncommon to repot when they are very small, with only their first leaves. This is referred to as pricking out the seedlings as the soil plugs is broken apart and you can use a toothpick or something like that to gently remove individual seedlings from the soil plug and them replant them individually.

Yes, thinning down to the most healthy seedling or two would be a good idea. Here is more information: https://www.gardeningknowhow.com/garden-how-to/seeds/thinning-seedlings.htm

As far as I know, planting them deeper will not hurt them. That said, they really need more light to keep them from becoming leggy, which will likely reoccur otherwise. This article should help: https://www.gardeningknowhow.com/garden-how-to/seeds/leggy-seedling.htm