As far as "would you like ..." and "do you like ..." as questions are concerned, the questions themselves are the same, but the tone and attitude are NOT. Using "would" is a more polite and indirect way.
Since it uses "would" to ask question, so you cannot answer with "I do". After all, people politely ask you question (or favor), you shall be politely answer with "I would"(direct answer).
Unfortunately, "I would" is not a choice. Instead, there is "I'm happy to" ("A" and "D" are obviously wrong). This is an indirect answer, yet it is more popular way to answer such a question in a day-to-day conversation. There are a few variations:
I would be glad to
I would be happy to
It is my pleasure
If you pay attention to people's conversation, people seldom use direct answer, unless it is in military or school (between teacher and student). "direct answer" gives people a feeling like a robot, yet "indirect answer" can express one's feeling better.
2012-09-21 06:44:04 補充：
Thank you for reminding me, I just cannot get rid of this BAD habit (Chinglish)!
2012-09-21 21:54:08 補充：
Language is very flexible, there is NOT a set rule for you to follow, but just a customary way to use. Grammar is a collection of customary use, not a rule. TO get used to these customary uses, you just have to read, speak, listen more. There is NO short cut or a book to get you there.
2012-09-21 21:57:22 補充：
As far as responding someone's asking or requesting, the basic idea is to be polite. You can answer it directly, or indirectly based upon your own preference.
2012-09-21 22:01:15 補充：
請求(request)和詢問(ask, inquire) are somewhat similar. Like the questioned sentence you have, it can be both "request" and "inquire". When sentence starts with "would you like ..." can be request or inquire depends upon the context, for examples:
2012-09-21 22:06:16 補充：
Would you like to have coffee or tea? (inquire)
Would you like to do me a favor? (inquire or request)
Would you like to do it on your own? (request, very polite)
Can you do it on your own? (request, less polite)
2012-09-21 22:09:48 補充：
I use ALL English answer is because I don't know how to type Chinese. Sorry for my short coming ! Usually, if I need to use Chinese characters, I will do cut and paste.
2012-09-22 01:07:08 補充：
As far as "should", "would", and "could" are concerned, besides they have their individual meaning, they also have different degree of politeness:
(less polite) should < would < could (more polite).
2012-09-22 01:08:54 補充：
Hence, you can use "Could you help me wash the car", even more polite than using "would".
You can say: Yes, no sweat (no problem), but with "yes" is kind of redundant in colloquial use.
2012-09-22 01:10:25 補充：
Would you like to have coffee?
No problem. 這樣回答很怪
You are right ! This is why I told you, you need to use feeling to get the difference, and use the proper response.
For that you can answer:
2012-09-22 01:11:44 補充：
Yes, thank you. (most common)
Yes, if you don't mind. (possible! but not as common).
2012-09-22 21:08:54 補充：
Yes, your feeling and saying is CORRECT.
As far as to answer it is concerned, you can use "yes, I would", or those indirect ways.
2012-09-23 08:16:22 補充：
That sounds about right !