1. A man is talking about something to the king. He said, Yesterday, I killed a big dragon with my kick."

2. There is a man talking to the king.
He told a lie, "Yesterday, I killed a big dragon with my kick."

3. In front of the king is a man. He told to the king a lie, "Yesterday, I killed a big dragon with my kick."

4. In front of the king a man is. He told to the king a lie, "Yesterday, I killed a big dragon with my kick."

[Are they all grammatical? Would you correct some errors?]

1. Where will you put the opening quotation marks?

2. The first sentence is fine. The second is actually a comma splice. How will you fix it?
https://owl.english.purdue.edu/engagement/2/1/34/

3. The first sentence is fine. The second is another comma splice. In addition, the word "to" is not needed in the second sentence.

4. Too many errors in this one!

From a grammatical standpoint, all four sentences are correct and understandable. However, there are some minor differences in terms of style and word order.

1. A man is talking about something to the king. He said, "Yesterday, I killed a big dragon with my kick."
This sentence is grammatically correct, but it may sound a bit awkward due to the word order. A more natural way to phrase it could be: "A man is talking to the king about something. He said, 'Yesterday, I killed a big dragon with my kick.'"

2. There is a man talking to the king. He told a lie, "Yesterday, I killed a big dragon with my kick."
This sentence is grammatically correct. However, it could be improved by using a more direct word order: "A man is talking to the king and telling a lie. He said, 'Yesterday, I killed a big dragon with my kick.'"

3. In front of the king is a man. He told the king a lie, "Yesterday, I killed a big dragon with my kick."
This sentence is grammatically correct. However, it could be rewritten to be more concise: "In front of the king, a man told a lie, saying 'Yesterday, I killed a big dragon with my kick.'"

4. In front of the king a man is. He told the king a lie, "Yesterday, I killed a big dragon with my kick."
This sentence is grammatically correct but sounds slightly awkward. A more natural way to phrase it could be: "A man is in front of the king. He told the king a lie, saying 'Yesterday, I killed a big dragon with my kick.'"

In summary, while all four sentences are grammatically correct, there are small improvements that can be made to make them more concise and natural.