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Yes. This article will help: https://www.gardeningknowhow.com/ornamental/bulbs/bgen/how-to-plant-a-flower-bulb-in-your-garden-after-winter-forcing.htm

Yes, but only after the threat of frost has passed. When you are ready for planting outdoors, trim off dead foliage and plant the bulbs about six inches deep in well-draining soil. Lilies need plenty of sunlight, so place in a sunny location. Your plant will need to be watered frequently during dry periods from spring through fall. Mulch will help conserve moisture. New growth should begin to emerge next spring (around this time). When growth is about 3 inches above ground level, fertilize with a 5-10-10 fertilizer (higher phosphorus than nitrogen). This article should help: https://www.gardeningknowhow.com/ornamental/bulbs/lily/planting-easter-lily-outside.htm

Dig up the lily carefully until the bulbs are exposed and gently extract it from the ground. Examine the root and bulb structure - look for natural divisions - this should be very evident because each new bulb will have its own set of roots/foliage. Divide the bulbs at these points with pruning shears. I would only take about one-third of the established plant for the new planting.

Then, follow the planting guidelines in this article:

https://www.gardeningknowhow.com/ornamental/bulbs/lily/planting-easter-lily-outside.htm

You can try deadheading. It is sometimes successful with lilies. As soon as the flower fades on the plant, remove it from the plant. The plant's main goal is to produce seeds, so if you remove the faded flower (which would have resulted in a seed pod), this can sometimes force the plant to bloom again in an attempt to produce seeds. Even if it does not bloom again this year, removing the faded flowers will cause the plant to produce bigger blooms next year. So it is a win-win situation.

Yes, your seeds will need to be dried. You can place them on a paper towel to dry throughly before storing them in an airtight container.

Here is a link about general seed collecting.

https://www.gardeningknowhow.com/ornamental/flowers/fgen/harvesting-garden-seeds.htm

Yes, these are the new starting bulbs. I would wait until they start to die off. Then you can dig them up. Here is an article for more information on their care: https://www.gardeningknowhow.com/ornamental/bulbs/lily/planting-easter-lily-outside.htm