1. Blue helps headaches.

2. Blue helps with headaches.

(Which one is correct? Are both correct? Which one is a common expression?)

3. What does the color purple do for you?

3-1. It helps me sleep better.
3-2. It helps us sleep better.
(Which one isa better answer?)

John, I have not heard either of those . But, both are grammatically correct.

#3.1 would be the correct answer since the question is directed at you.

Both sentences in questions 1 and 2 are correct grammatically, but the more common expression is "Blue helps with headaches." This sentence implies that the color blue has a beneficial effect on relieving headaches.

Regarding question 3, both options 3-1 and 3-2 are grammatically correct, but the better answer would depend on the context. If "me" refers to the individual answering the question, then option 3-1 ("It helps me sleep better") would be more appropriate. Conversely, if "us" refers to a group of people responding collectively, then option 3-2 ("It helps us sleep better") would be a better answer.