The ad- in adhuc adds nothing to its meaning. Huc alone means “to here, hither(to)” (just as illuc means “to there, thither, far from both speaker and addressed party”. There is istuc too, which means “to where you are”).
When the meaning of huc alone began watering down to the point that it was even used almost like a preposition (see the example at the above link: commigravit huc viciniae “moved into this neighborhood”), ad- was added as a strengthening, especially to emphasize the whole extent of the motion:
To fully clarify the first point in your list, one should add that it is normal for spatial adverbs to be used for time too: “to here” becomes “up to now” and “so far” very easily (notice that in English too, “far” has a basic spatial meaning, but I have just used it for time.)
I’d like to add that the most basic word that means “now” in modern Italian, adesso, comes from ad ipsum, a colloquial form which replaced adhuc when most h*c demonstratives fell into disuse.
I understand why the second meaning
- [2.1] again; [2.2] furthermore; [2.3] moreover; [2.4] besides (used in scholastic debates to introduce an additional point in one's argument)
makes you wonder: the basic meaning of “further(more)” in English is that of a departing motion, not the approaching motion of adhuc, and this might be confusing. However, you have to remember that ad- means also “addition”, and this is what we have here: not “to this (place)” but “in addition to this (fact)”. It is not a later development, this meaning of addition was there from the beginning: already Plautus has addam minam adhuc (Plaut. Truc. 5, 18)
What is a later development, of course, is its use as a filler in speeches.
As to number 3:
- [3.1] even as, [3.2] while still
Since adhuc encompasses the whole (possibly metaphorical) interval being traversed, a meaning of “duration” is a natural development too: “still”, “while still”, “while yet”, “as yet” are explained in this way. And “even as” is explained either as an evolution from the meaning “to the point that”, or as a contrastive usage which is also present in the English “while”.
Reading both linked entries in Lewis & Short will give you more insight.