How do the concepts of 'wyrd' and 'fate' influence or affect Beowulf's actions throughout the poem?
My only issue with your question is that the Anglo Saxon concept of "wyrd" and our word "fate" mean precisely the same thing. (The more "Christian" word for it all would be "providence.") Once you begin thinking of it as wyrd/fate, it's much easier to understand.
There are many quotes that can exemplify this idea. For example, even though Grendel was notorious, he could have killed more men, but it was wyrd/fate that kept him from doing so. The narrator says that Grendel would have slain more
except God in his wisdom and the man's courageous spirit had withstood that wyrd and him. The Lord ruled all the human race as he still does.
There is also no way of getting around the Christian influence of wyrd/fate here in the hand of "providence." Note the words "God" and "wisdom" and "the Lord" and "ruled." One god. Monotheism. Christianity. Not the original paganism of the Anglo Saxons. Here it is precisely God that moves the actions and the doings of all men. There is a plan in place for what happens on the earth. And yet, all things that happen are due to free will. In this regard wyrd/fate is more than just some kind of "blind force" that determines everything. Free will prevents that.
Another perfect example of wyrd/fate can be found later in the book and is said by Beowulf himself:
Each of us must await the end of his path in this world, and he who can, should achieve renown before death! That is the best memorial when life is past and a warrior's days are recounted!
Here Beowulf reflects on the "path" that everyone must take in the world. Note the idea of free will in the phrase "who can." Beowulf is saying that if you can achieve fame or "renown" before death by doing something good for the country and its people, that is the best epitaph anyone can have. This not only reflects Beowulf's belief in wyrd/fate, but also his impression of immortality.
There are several examples of this. One example is when Beowulf decides he will fight Grendel barehanded. My translation (Burton Raffel) reads "Fate will unwind as it must." Later when Beowulf fights the dragon, my translation reads: "... And for the first time in his life that famous prince fought with fate against him, with glory denied him. He knew it, but he raised his sword and struck at the dragon's scaly hide..."