Yes, you could. /Yes, you can.

[Exalted Father]

How do you please answer the following questions "could I have a cookie?"

 

[Tarheel]

Either:

Yes

OR

Yes, you may.

 

[Tarheel]

Please capitalize the first word of every sentence.

 

[emsr2d2]

How do you please answer the following questions question "Could I have a cookie?"?

1. Yes, you could.
2. Yes, you can.

Make sure you put the sentences you're asking us about in the main body of the post as well as in the title. Note my changes above to your main question.

The question itself is a little unnatural. We would ask either "Can I have a cookie?" or "May I have a cookie?"
The simplest answer to either question is "Yes" (or "No"). If you really feel the need to extend the answer, say "Yes, you can" in response to "Can I have a cookie?" and "Yes, you may" in response to "May I have a cookie?"