Even in Belgium, one of the highest density countries in the EU, most existing and newly built houses are semi-detached, with about twice as much semi-detached + detached houses as there are terraced houses.
In France, terraced homes are rather uncommon outside the North close to Belgium, and old city centers. In fact, I don't even know if we have a name for detached houses, as far as I know they're just called "a house" while a terraced house is a "city house".
So I don't have the numbers for all of the EU but I don't think most homes are actually terraced homes in the EU.
And people do have grass lawns, but only where grass actually grows without too much care needed. Where I come from on the coast grass doesn't grow well on the sandy ground and lawns are uncommon, but a few kilometres inland if you don't do anything you get a mostly-grass lawn, with a lot of clover, daisies and often orchids growing in it.
Single family homes are both expensive and uncommon as land is generally more of a premium.