What are some external and internal conflicts that Beowulf faces?
Concerning conflicts in Beowulf, external conflicts abound. Beowulf fights Grendel, Grendel's mother, and a dragon. He also faces skeptics, such as some of Hrothgar's men, when he arrives in their homeland and announces that he is there to solve their monster problem, which, of course, they haven't been able to solve. He also faces the problem of his loyal followers not being so loyal, or at least not so brave--when they refuse to help him fight the dragon, for instance.
In short, Beowulf is good and noble and honorable and just and he is in almost constant conflict with evil and dark forces, for the most part, and envy and jealousy and cowardice, in minor instances.
Concerning internal conflicts, the nature of a hero in an epic like this one, written at the time it was written (Anglo-Saxon England), is such that internal conflicts are anathema, pretty much nonexistent. Beowulf is perfect or at least nearly perfect. He is good and righteous and almost all powerful, and he knows it. He knows what he does is righteous, and he knows he can do it. He does not suffer from self-doubt or any questioning of his purposes or questioning of the consequences of his actions. Beowulf is an ideal hero. He, at least for the most part, does not have inner conflicts.
In other words, I cannot say for sure that no internal conflicts exist in the whole of the Beowulf epic. I can say that, for the most part, a hero like Beowulf does not have inner conflicts. He is on the side of goodness and God and justice, and one cannot question that--at least not for many centuries after Beowulf was written.