What's the difference between seem & appear in this sentence?
It appears/seems that the man had been murdered.
Are there any specific structures for using these verbs?
Very little difference.
"Appears" is a very slightly more formal word than "seems." It might be more likely to be used in a professional context, such as in a coroner's report.
In addition, "seems" may mean that you have used more than visual information to come to your conclusion. Someone may have said something that, in addition to the evidence you see, leads you to believe that the man was murdered.
Lastly, while neither word indicates that you are certain he was murdered, "seems" conveys slightly more confidence in this idea. If you use "appears," you give the impression that you are only stating the facts and wish to remain neutral about the conclusion. It may even suggest that you continue to seriously consider the possibility that he was not murdered.