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While there is no real definitive answer here, I would go along with your suggestion (bringing in soil and planting with grass). There is no way to prevent the tree from dropping nuts and unless you want to spend all your time cleaning up your bed, it would probably be just as easy to rake the area clean whenever needed.

You can grow any tree in a container as long as you have enough room for the roots and can provide the water it needs. If the tree is just a sapling, you can likely keep it in a container for at least a few years before its space and water needs become more than you can provide.

You want to give it at least 40 feet of spacing from the house as this will be its potential spread when fully grown. The spread of the canopy in trees reflects the spread of the roots, so if you plan for the canopy, this will also take care of the roots.

While there is a chance you have a sterile tree, this would still not explain the lack of blooms. The amount of time you have had it tells me it has been flourishing. Normally, these trees will develop blooms within the first 4 years and begin setting seed within 8. Perhaps there is a problem with pollination or you could try add phosphorus to the soil, such as bone meal. I am sorry I cannot be of more help to you, as this has me baffled as well.

I am not certain why your tree has not produced blooms, which of course affects its ability to produce chestnuts. While there is a chance you have a sterile tree, this would still not explain the lack of blooms. I am assuming that it is planted in an area receiving sun, as the amount of time you have had it tells me it has been flourishing. Normally, these trees will develop blooms within the first 4 years and begin setting seed within eight. Perhaps there is a problem with pollination. I am sorry I cannot be of more help to you, as this has me baffled as well.

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