may I ask if 敢于 and 勇于 are interchangeable words? In English, both of them mean dare to, have the courage to do something. I looked up some sentences involving both words and it seems to be used in a number of similar situations. The only difference that I seem to notice based on the sentences I read is that 敢于 carries the meaning of dare to fight for something or do something while 勇于 carries the meaning of having the courage to face difficult times. Not sure if it's correct. For eg, is it 敢于承认错误 or 勇于承认错误.
You already found the answer in your English interpretation
敢于 = dare to
勇于 = have courage to
敢於挑戰強權 (dare to challenge power)
勇於挑戰強權 (have courage to challenge power)
To find the difference between '敢于' and '勇于', you only need to find out the difference between 'dare to' and 'have courage to'
'Dare to' doesn't always equal to 'have courage to'
You may dare to do something because you are confident or you are willing
敢于对抗强敌 can mean 'you are brave at facing strong enemy' or 'you are confident in facing strong enemy'
勇于对抗强敌 just mean you are brave at facing strong enemy
"敢于尝试新口味" = "dare to try new taste" (it doesn't require courage to dare, it just requires willingness)
"勇于尝试新口味" implies trying new taste require courage, which is too exaggerated, the worst thing can happen is you don't like the new taste
"敢于起用新人当主角" = "dare to use new face for the leading role"
"勇于起用新人当主角" implies using new actor for the leading role require courage, but more often than not, it just requires willingness on the director's part to give new actor a chance