1. Did you know? + Where did he go?

2. Did you know where he went?
3. Did you know where he had gone?
(Which one is similat to #1?)

4. Do you know? + Can he play the guitar?
5. Do you know if he can play the guitar.
(Are both the same?)

6. Do you think? He can play the guitar.
7. Do you think if/whether he can play the guitar?
8. Do you think he can play the guitar?
(Is #2 not correct? #6 can be changed into #8, right?)

Both 2 and 3 mean about the same as 1. The difference in tenses indicates the time when he was gone: in 2, where he went and was at the same time as "Did"; in 3, where he went at a time definitely previous to "Did."

4 and 5 are the same, yes.

6 and 8 are the same. 7 is incorrect.

1. The question "Did you know? + Where did he go?" is asking if the person being addressed has knowledge about where someone went. It is a combination of two separate questions: "Did you know?" and "Where did he go?"

2. The question "Did you know where he went?" is asking if the person being addressed has knowledge about the specific location where someone went.

3. The question "Did you know where he had gone?" is similar to the third question in terms of tense, but it emphasizes the past event of someone going to a certain location.

Regarding the similarity to #1, the question "Did you know where he went?" is the closest in meaning to the combined question "Did you know? + Where did he go?" since it specifically asks about where someone has gone.

4. The question "Do you know? + Can he play the guitar?" is a combination of two separate questions: "Do you know?" and "Can he play the guitar?"

5. The question "Do you know if he can play the guitar?" is asking if the person being addressed has knowledge about someone's ability to play the guitar.

Both questions #4 and #5 are similar in meaning as they both seek information about someone's ability to play the guitar. The difference lies in their structure and wording, but the overall intention is the same.

6. The statement "Do you think? He can play the guitar" is not a grammatically complete question. It seems to be missing a verb or auxiliary verb before the pronoun "he."

7. The question "Do you think if/whether he can play the guitar?" is asking for the person's opinion or belief about someone's ability to play the guitar.

8. The question "Do you think he can play the guitar?" is a direct question asking for the person's opinion or belief about someone's ability to play the guitar.

Regarding the correctness, question #2 ("Did you know where he went?") is grammatically correct and has a clear meaning. However, question #6 ("Do you think? He can play the guitar") is not grammatically correct without any verb or auxiliary verb, and cannot be changed into #8.