I love this stuff. :)
1) It is quite likely that the Borg cube would not raise its shields when facing one individual being. They didn't raise their shields when the Enterprise first encountered them either, allowing the away team to beam aboard and away again. The Borg hive mind doesn't pay much attention to microscopic threats; it lets its subsystems do that, just as you don't consciously fight infections.
2) At the same time, the Dalek would predictably say, "YOU - WILL - SERVE - THE - SUPERIOR - DAAAALEK - RACE. YOU - WILL - OBEY - OR - YOU - WILL - BE - EXTERRRRMINATED." The Borg assimilate. The Daleks simply kill whatever they can't enslave.
6) I've read comments about how the Borg's nanoprobes might be able to penetrate the Dalek's shell by finding microscopic openings. But the Borg can only assimilate a living creature by injecting nanoprobes into its body, and they can only assimilate a computer by connecting to an input/output port of some kind. But they can't inject anything through the Dalek's shell, and the Dalek's aren't computers. The Daleks aren't even cyborgs; they are basically mini dreadnoughts piloted by an organic life form inside. The most assimilation the Borg could do would be to scan the Dalek with their sensors, adding that data to the Collective (which, by the way, was the only type of assimilation the Borg did when we first saw them; the rest was added by later writers, and I think it made them less impressive rather than more).
8) The Borg would doubtless continue to attempt to adapt their weaponry to their ongoing scans of the Dalek's armor. We have seen hand-held (but large and high-tech) weapons destroy Daleks, so it just becomes a matter of finding the right weapon. This becomes a race with step 9.
9) Since the Borg's adaptive shielding isn't one technology, as has been pointed out, but rather is the result of the Borg's constant information assimilation and adaptation process, there is no "adaptive shielding" to learn, even if there were a way to learn a species' technology by studying its DNA. However, this might be six of one, half a dozen of the other -- by analyzing Borg DNA, the Dalek would realize that this was a phenomenally adaptive species and gain insight into how the Borg were adapting their shields.
10) I don't think Dalek weapons are built to be modulated in this way, as the typical Dalek response to "My weapon can't penetrate this shielding" is not "Modulate the frequency"; it is either "Use a bigger weapon" or "Destroy it another way." If the Dalek has no other weapons it may analyze the structure around it and start attacking that with strategic shots, and if the Borg have shielded the structure too, the Dalek would probably Emergency Temporal Shift out of there ... then come back with a lot more Daleks with a wide variety of weapons, this time redesigned with randomly modulating frequencies. I could be wrong, of course -- the Dalek might just say, "CONTINUOUSLY - ADAPTING - ENERGY - SHIELDS. HOW - QUAINT. THE - DAAALEKS - HAVE - CONQUERED - SEVENTY-THREE - SPECIES - WITH - SIMILIAR - ABILITIES. ACTIVATING - WEAPON - RANDOMIZER."
I do still think the Daleks would defeat the Borg, though. Although both of them destroy anything they don't find useful, the Borg's idea of useful is based on what they can use to improve themselves; this means that they let things live longer so they can study and assimilate. The Daleks' idea of useful is based on what they can use, in the sense of using tools, and when a tool isn't working right they destroy it. They often destroy their tools once they're done with them, too. Also, they aren't cold and calculating like the Borg; the Daleks have been known to abandon all tool-using and merely destroy out of anger or revenge. Unfortunately, "shoot first and ask questions later" tends to beat "let's scan it first to see if we can learn anything useful."