Bernard De Cluny was a 12th century Neoplatonic poet and monk of the Benedictine Order in Cluny. He wrote De contemptu mundi. His tenet was a condemnation of searching for happiness in earthly pursuits. He advocated a heightened morality. If applying the principals in De contemptu mundi to Beowulf and Bede's "The Sparrow in the Hall" analogy, you might look at the death and funeral scenes that conclude Beowulf and compare this to the sparrow's brief sojourn in the comforts of the warm "banquetinghall."
#5, I disagree that Bede shows contempt for the world. The sparrow flies out of a blizzard into a warm hall; for that brief period, he is warm and safe. Then he flies out again and is assaulted by the blizzard. Even if the hall -- life -- is fleeting, is it not entirely preferable to the blizzard in this analogy? I might even argue that Bede shows contempt for the spiritual world!
Contemptus mundi is a phrase that is used in religious works to develop a key Christian theme in both of these texts. The contempt for the world is something that is a key tenet of Christianity, as we are meant to focus on what is to come rather than accumulating earthly wealth and treasures in this temporary stage of our existence. We can see this in the way that death is treated and viewed in both texts, as the various characters live their lives in full awareness that there is an afterlife that they need to think about and be aware of.
Both works express a contempt for the world. The comment about the sparrow in Bede, ironically, implies that the world is a pleasant place but also implies that our existence in the world is ephemeral and fleeting. One of my favorite moments in Beowulf comes near the very end of the poem, when the poet describes what happens to the treasure after Beowulf is cremated:
They let the ground keep that ancestral treasure,
gold under gravel, gone to earth,
as useless to men now as it ever was.
Even earthly treasure, in other words, has no real permanent value. What matters instead (the poet implies) is our existence in the next world.
I think contemptus mundi is a little problematic in Beowulf, as the hero's deeds, and his reputation for achieving them, are still very important to him. It is a sort of tension between pagan virtues and those of Christianity, which does, as the question indicates, reject worldly things, at least in theory. As for Bede's famous "sparrow through a mead hall" quote, he certainly emphasizes the fleeting nature of life, and the importance of embracing Christianity, which gives hope for the hereafter, but here, as in Beowulf, I'm not sure he's quite at the point of contemptus mundi. Certainly much of the rest of Ecclesiastical History is full of political squabbles and other worldly affairs.
In both of these works, the authors are saying that things of the world are fleeting. Therefore, we should not really take them too seriously. It's like the saying from the Bible about not caring about your treasure on Earth because moths and rust can corrupt them. The same is true in these works -- they are saying that things that seem glorious and important on Earth really aren't.