Both responses are grammatically correct, but they have slightly different meanings and tones. The response "I know" (option A) is a simple acknowledgement of the compliment. It is a straightforward and neutral response that indicates agreement. The response "And don't I know it" (option B) is a more enthusiastic and perhaps slightly playful response. It implies that Chet is well aware of how lucky he is to have a good woman, and suggests that the speaker is happy to hear the compliment and agrees with it. So, the correct response would depend on the intended tone and level of enthusiasm.

Both are correct. For this expression/idiom, starting the sentence with "and" sounds normal. I don't use that expression but I have family and friends who do. In writing, I think the second sentence comes off as a little more engaging and expressive, but if spoken, you could make both sentences sound equally expressive.

both however B. does not need the and at the beginning as you don't typically start a sentence with and

Both are correct. A is the more straightforward way to say this. B is more idiomatic.