horse chestnut or sweet chestnut?
Neither sounds like a patio plant to me
They are yes.
I haven't heard of a patio version but there may be.
Are these the ones http://www.amazon.com/5-6-ft-Chinese-Chestnut-Tree/dp/B00DG7X9FC
If you read the information more carefully you'll see that they're supplied at 5-6ft tall - they grow to 40 - 60 ft.
Yes grew one from a conker in fact I still find ones growing with the conkers I threw away.They are easy to grow but you have to have a big garden to grow one.
Whose ad is it?
If it's a proper nursery it will be OK. If a proper fruit and nut tree nursery hasn't got it then it's most unlikely you'll get one from Amazon/ebay or similar