Duo's answer is more common in England, perhaps because its meaning matches more closely with the Spanish version i.e. that there are various things wrong with the car as opposed to one particularly bad 'damaged bit'? I think both are used equally around the world though. I agree with AurosHarman that for dents, we'd probably specify those as 'damage' usually refers to more serious (and expensive) damage.
Defects are flaws that are innate, but damage occurs to something from an outside source. http://dictionary.reverso.net/english-spanish/defects
Sometimes a noun which is used as singular in one language is simply used as plural in another.
Not sure what region you're from, but it sounds extremely peculiar to me. (My main exposures are mid-Atlantic for twenty-one years and SF Bay Area for sixteen.) As I said, it's interpretable as likely meaning "a lot of", and the structure isn't technically ungrammatical, but I can't imagine anyone using "much" instead of "a lot of" in this sentence. Unless they were a Renaissance Faire nerd who couldn't drop character.
It's to do with how we use much/many in English. This site has a good explanation:
Much/many = questions and negative clauses (and in positive clauses when modified with 'so', 'as' or 'too')
A lot of / lots of = positive clauses (but I think they're fine in negative clauses too)
I have a lot of water (not: I have much water)
There is lots of damage (not: there is much damage)
I don't have much water, How much water do you have?, I have as much water as you
Intensely weird, I love that :) In defence of the "much" suggestion though, it is exceptionally normal in formal situations. To quote Ellelingo's source: "In formal texts, however, much / many are also common in positive clauses." Newspapers and the news are good examples: eg. You might read/hear "The hurricane has caused much damage. Many houses were destroyed."
Definitely not. You can only use singular "mucho" to express "a lot of" with a mass noun. Hay mucho arroz. There is a lot of rice. Daño is a count noun, like apples. You can't say: "Hay mucha manzana," to mean, "There are a lot of apples."
It may help to think of daño like English's similar count-noun, "wound", rather than "damage".