Yes. Adjective endings depend on the noun's gender and case. And they only decline when they come directly before a noun to describe it: - Ein rotes Buch. - Das Buch ist rot. (Not "Das Buch ist rotes.")
Also, the adjective takes a different ending depending on the type of article before it: - Das rote Buch. (Not "Das rotes Buch.")
In the US that would be considered affected speech. Other places probably fine.
"You have a red car?" Does not work either, this would be perfectly acceptable within a conversation in English
"You have a red car?" works but it isn't the best form. You might say "You have a red car?" if you're trying to confirm that fact, for example, but "Do you have a red car?" is the standard question form.
I disagree, people would get the meaning but you need to say 'Is your car red?' Or 'Do you have a red car?'
"Is your car red?" doesn't quite work because it assumes you HAVE a car. "Do you have a red car?" does not assume that.
Did you get it wrong for that? Report other. While not entirely common in all English speaking places, it still is correct. Well, as far as I was taught anyway. I believe it may be an older form of English
Could this also be correct: "hast du das rotER Auto? since there is a definite article (das)?
No, that would be Hast du das rote Auto? I have a strategy for memorizing all this, if you're still looking http://gregreflects.blogspot.com/2015/02/how-to-memorize-german-cases.html
Have you a red car? is correct English, albeit a bit old fashioned and posh sounding: "have you a red car, old chap? Smashing!"
so when do you use rot, roten, rotes....I don't seem to see any explanation...it's doing my heading
When the adjective is not in front of a noun, it doesn't need an ending.
When the adjective is in front of a noun, it needs an ending according to some rules.
Duolingo has an explanation for this lesson on the web version (scroll down): https://www.duolingo.com/skill/de/Colors
By the way, the English phrase is "doing my head in".