"No star is brighter than the moon."
Proper Comparative Structure
Correct Use of "Than"
Definite Article ("the moon")
"No star is more bright than the moon."
"No star is brighter then the moon."
"No star is brighter than moon."
More bright is wrong since bright becomes brighter in the comparative verb form.
"Than" should be used instead of then.
Lastly, the article “the” should be used as the sentence is mentioning the moon, which is specific.