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This plant needs shade. The afternoon sun is too strong for it. Move it to a spot that only gets morning or filtered sun.

You may be lacking phosphorus. If there is a lack of phosphorus in the soil, plants will have little to no blooms. You can either use a phosphorus rich fertilizer or add some bone meal to the soil.

Up the watering and give it some phosphorus rich fertilizer or add bone meal to the soil to help encourage blooming.

You would cross pollinate. This article talks more about how:
http://www.fuchsiaflower.co.uk/hybridizing.htm

Yes, these pods contain seeds and you can try starting the seeds. This article will explain how:
http://www.bonsaigarden.net/growing_fuchsia_from_seed.html

Here is an article that you may find helpful: https://www.gardeningknowhow.com/ornamental/flowers/fuchsia/fuchsia-winter-care.htm

If it is a hardy fuchsia variety, then If you want to leave it in the garden, cut it back and give it a generous covering with mulch over winter.