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The best thing to do would be to store them in a sheltered place, like a garage or a shed. If left outside, the water and temperature fluctuations will crack them.

Most people sterilize their containers before storing them by wiping them down with a weak bleach solution. This way if your plants had some kind of disease, the disease does not overwinter as well.

Broken pots, Styrofoam peanuts and gravel all make excellent drainage mediums.

Typically, if you are downsizing a plant, you will be doing some root pruning. This article will help you with root pruning:
https://www.gardeningknowhow.com/houseplants/hpgen/prune-roots.htm

Anytime you are repotting a plant, it is susceptible to transplant shock, but even more so when you are also root pruning. This article will help you with that:
https://www.gardeningknowhow.com/plant-problems/environmental/learn-how-to-avoid-and-repair-transplant-shock-in-plants.htm

If you can let me know what kind of plants they are, I can give you further help on how to handle splitting them.

Yes, or you can even use Styrofoam peanuts instead of rocks in the bottom of pots. Depending on the pot size, some people also prefer to drop another smaller plastic pot (with drainage holes) inside the ceramic one. This could also sit on top of the rocks. Anything you can do to keep the plant roots from continually sitting in water is a good idea.

Try looking at sedums. They have very shallow roots and would like a bowl.

It depends on the kind of tree you use in the container whether they will need to come in or not. If you plant something that is for your zone or higher, then it will need to be brought in for the winter. If you choose one that can survive in zones lower than your own, than it can stay out.

If you have a plant that can stay outdoors in containers, it is still a good idea to store it near a wall and cover the plant with burlap or a sheet to help protect it from drying winter winds.

If it needs to come indoors, how you store it indoors and if it needs dormancy will greatly depend on what you grow.