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flat end down, pointy end up.

The seeds should be planted indoors as soon as possible, because they are though to lose viability quickly. The seeds need to go through a cycle of cool-warm-cool to induce germination. Sow 2mm deep in a mix of compost and peat, and water. Place the container in a cool, moist spot or inside a plastic bag in the refrigerator for 3-6 weeks. Then, move them to 13-18 degrees C for 3-6 weeks, then back to the fridge, then back to the warmth. If there's no germination, go through the cycle again. Then, keep them as an indoor potted plant until you can plant them outdoors after the risk of frost in spring.

Either way will be fine, actually. You can leave it, or cut it. This article will give you more information on the care of these plants: https://www.gardeningknowhow.com/ornamental/flowers/himalayan-lily/himalayan-giant-lilies.htm

Some types of Asiatic lilies have furry buds and little furballs where the leaves attach to the stem. This is perfectly normal! Your plants look healthy and you should be rewarded with some beautiful flowers!

https://www.gardeningknowhow.com/ornamental/bulbs/lily/planting-asiatic-lilies.htm

Stem cuttings are the best means of ensuring the sport's characteristics in the next generation. Seeds (bulblets) are not reliable carriers of the sport's genetics. It sounds like an interesting project.

Yes, it is best to dead head both most types of Lilies.