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This article will help you with this: https://www.gardeningknowhow.com/edible/vegetables/pepper/pepper-blossoms-falling-off.htm

No, you will need to harvest the seeds and dry them.

Here is a link that will help you.

https://www.gardeningknowhow.com/edible/vegetables/pepper/harvesting-pepper-seeds.htm

This could be insects or fungus problems.

Always a good idea to spray plants before bringing them indoors.

Washing with a spray of water and then a treatment with Neem Oil is a good idea.

Neem Oil works as both an insecticide and fungicide; it is safe for people and pets.

Here is a link with more information.

https://www.gardeningknowhow.com/plant-problems/pests/pesticides/neem-oil-uses.htm

There can be a few reasons for distorted peppers and it can be quite common in pepper plants.

Environmental changes, inconsistent water, lack of nutrients and a plant that is getting quite old may all be reasons.

Make sure you are using good quality fresh potting soil each season.

Save seeds from the healthiest peppers.

This is how I plant my pepper transplants. I remove the first set of leaves and plant deep.

Not very deep at all. Place your seeds on the surface of the soil, then cover them over with a scant 3 millimeters of soil. You just want the seeds just below the surface.