'¿Te gusta la roja?' should be accepted as well
Yes, both possibilities "el rojo y la roja" are accepted, because nobody can know, what is meant without any context.
Why isnt "Te gustas el rojo" correct?
Gusta is different. It means pleases, and not really like. The red one is the subject of the sentence and "you" are the object. So the Spanish sentence is more "the red one pleases me."
Can someone explain why "Usted le gusta el rojo" was not accepted?
It would need to be "a usted le gusta..."; you're missing the "a".
"Le gusta a usted el rojo?" should be accepted. The question contains no indication as to whether "you" is formal or familiar, so both should be considered correct.
I THINK you need to start with the "a usted".
But you probably need a better grammar source than me.
why do not accept llevar as in to take the clothes?
The question could be do you like the red painting I have on my wall. Or maybe he is asking if she likes the red necktie he is thinking about wearing.
This question doesn't say anything about "taking", it's asking about "liking", so llevar wouldn't make sense, regardless of whether we're talking about clothing or not.
Why is 'lo rojo' wrong here