Welcome to the Downs,
Hobbitt_Fan, enjoy being dead!
I'm not sure that Beorn was
meant to be an enigma like Bombadil - we have to remember that
The Hobbit originally was written as a stand-alone children's book, not as part of the Legendarium established in the earlier Silmarillion tradition, and thus contains all kinds of elements that aren't exactly 'canonical' within that tradition (cockney Trolls, giants in the Misty Mountains and a werebear of somewhat fluctuating stature) coexisting peacefully with borrowings from the matter of the Elder Days (Elrond, Gondolin, the Necromancer). Only when Tolkien decided that TH and its sequel, LotR, were after all set in the same world as the Silmarillion did such elements as Beorn become a problem. (Taking another character, I'm pretty sure the Prof had no idea Gandalf was a Maia when he wrote TH; he only 'discovered' that later, trying to make sense of what he'd written earlier.) But that's of course meta-reasoning and will most likely be considered spoilsport by some of our dear fellow Downers (present company included).
I think you're quite right about the similarities between Beorn and Beowulf, especially considering the etymology of the latter's name ('Bee-wolf', a kenning for bear). This was also discussed in the thread
The Might has linked to, as well as echoes of Nordic berserker legends in Beorn's character.
As for the origin of Beorn's shape-shifting abilities and his possible connection to Radagast, another explanation of this was suggested by yours truly on
yet another Beorn thread. [/shameless self-plug]