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Yes, you can do this.

Calla lilies will not survive in your area over winter. Here is more information: https://www.gardeningknowhow.com/ornamental/bulbs/calla-lily/calla-lily-winter-care.htm

Allow the seedpods to dry on the plant and then harvest the seeds. Plant the seeds in moist, but well-draining, soil. While you can grow them from seed, you should know that they will take up to three years to flower. Therefore, it is generally better to propagate these plants through division.

If you're not saving seeds, you can simply cut the seedpod off or leave it. Of course, if you save them, keep in mind that seed grown plants will take longer to produce flowers.

Yes, these are seed pods, which can be used to grow additional plants. Seed pod are ripe once they turn yellowish and go soft. At this point, you can harvest the pods. Remove the pod from the plant and break it open. Then, take the seeds from the pulp using a plate or collander to catch them and rinsing under water. Dry the seeds and store them in a dry, cool place or plant right away. You can also choose to save the seeds by cutting off the dried seedpod (turns a orange, gold or light green color) and storing the seeds in an airtight container until ready to plant. Of course, seed grown plants will take longer to mature and produce flowers when planted this way verses offsets.

I would set it on a pebble tray filled with water. This will help keep humidity up around the plant. Misting the plant will also work, but you may find that it encourages fungus to develop on the plant.