Being, so, no such. If "so" isn't an option for 2 I would go for "that" 1. There is a fine distinction. As I read the question I would have said "are" but "being" is better. 3. No such thing is a standard phrase

The country's chief exports are coal, cars and cotton goods, cars being the most important of these. 'being' is correct. You cannot repeat the verb 'are' in the same sentence, but if you made it two separate sentences, it would be grammatically correct. ie 'The country's chief exports are coal, cars and cotton goods. Cars are the most important of these. 'Being' is a gerund, a type of noun formed from a verb, usually by adding -ing. - eg: eating, working, playing. A similar example - 'The most popular sports are football and basketball, football being the most popular;. My son walked ten miles today. We never guessed that he could (should) walk that far. This is an odd sentence and is not grammatically correct. I think it should read 'could' - which means capable/able to. 'Should' is used when telling someone they have to do something. 'You should make sure you go to your class on time'. In the example 'that' is correct - it means 'so'. You can think of it as 'Wow, he walked ten miles? I didn't think he would be able to walk so far!' 'Land belongs to the city : there is no such thing as private ownership of land.' 'Not such' and 'not such any' are not grammatically correct. Also, 'no such a thing' is not correct. You could say 'there is no such thing as a' but it would appear a little clumsy in this sentence.