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Shaping is just a matter of pruning until the shape of the plant is pleasing to you. However, try not to take more than a third of its growth off the branches. Also, be sure to cut any dead or unsightly limbs. It is best to wait until late summer or early autumn to prune.

It would be a race to the finish for them as the Horse Chestnut is also alleopathic (poisonous to other plants). Typically, the alleopathy of these plants can be greatly reduced by making sure that their leaves and fruits are removed from the ground in the fall. This typically reduces the area of alleopathy to just a few feet around the trunk. If you feel you can be diligent about that, then these two trees can be planted close to each other.

This article should help with that: https://www.gardeningknowhow.com/ornamental/trees/horse-chestnut/how-to-grow-a-horse-chestnut-tree.htm

I would recommend doing a local search for your area to find any retailers or even mail-order catalogs. Your local garden center may also be able to help. You can also check out eBay. In my experience, eBay is actually a great place to find unusual plants/seeds. Just check the feedback on the seller before you buy.

Tree roots generally reflect the canopy, so as wide as the canopy goes, that is normally how wide the roots go. That being said, trimming the canopy will not reduce the size of the roots. They will simply grow to be what the canopy should be when not pruned.

Whether or not it is a danger to your foundation is a question for an arborist who has looked at the tree in person. Most trees are actually pretty lazy and their roots will not put too much pressure on foundation walls UNLESS they become crowded. Without physically examining the tree, it is hard to say whether your trees roots are crowded.

I would recommend having a arborist come in and look at the tree. They will tell you whether you need to remove it or if it is fine where it is.

You could place a stake of some sort in the container and lightly tie the stem to it, maybe with a piece of pantyhose to keep it from damaging the tender stem as it grows.