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Here is an article or two that you may find helpful: https://www.gardeningknowhow.com/special/containers/choosing-containers-for-potted-environments.htm
https://www.gardeningknowhow.com/garden-how-to/soil-fertilizers/soilless-growing-mediums.htm

I would treat them for pests as small pests can hide in the leaves and it just takes a few to create a population once they are inside.

If possible, you may want to consider acclimating the plants as well. This article will help with that:
https://www.gardeningknowhow.com/houseplants/hpgen/using-pesticides-and-other-chemicals-on-your-houseplants.htm

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.