A lot of questions. I am no one official, but here are my thoughts:
RANGE: As written I do not believe that there is a range limit to how far you set up a nurturing conduit. However the range of your healing spells will functionally have some impact and make it meaningless in most situations to set one up on two allies, on that hill, waaayyy over there at the limits of what you can see clearly.
HOW MANY CAN I HAVE UP: Since it doesn't say, I would assume you can put as many up as you want. As a guy who is conservative about how powers should work I think that maybe they should have put some limit on it (a maximum number of links equal to your Wisdom or Proficiency modifier?). But they didn't. So if over 6-7 rounds of combat you want to create 6-7 conduits (paying the bonus action each round) I think you can rock on. The targets all have to stay within 30' of their "healing buddies" or the link is broken.
HOW DOES CHAINING THE CONDUITS WORK: PART 1: I believe your first two examples are correct. A-B & A-C would result in both B & C getting "bonus" healing when you cast a healing spell on A. But if you go A-B & B-C and then heal A ... only B gets bonus healing (because a spell was only cast on A).
HOW DOES CHAINING THE CONDUITS WORK PART 2: This is the only part that i find confusing. I believe you can only reap the healing benefit of the Conduit once per casting. So if you have A-B-C-D and all they get healed with a single Prayer of Healing (or other mass heal spell) then I believe they would all also benefit from the Conduit of Healing
once. I agree that the wording is murky but that interpretation is more or less in line with the power levels of the 6th level clerics and especially roughly comparable (if more complicated) than the similar Belisardan healing ability granted at 6th level. The language of the power is:
On page 63 of the Codex 5E Henry & Co wrote:
any time you cast a spell of 1st level or higher that restores hit points to one of those two creatures, the other is also healed...
A really strict reading of that might imply that power only activates when a single target healing spell is cast. But IMO that's almost certainly too restrictive. I think the right answer is you get the bonus healing once per casting no matter how many conduits and targets overlap. Anyway, this is my best guess.
HOW DOES THIS INTERACT WITH AURAS OR REGENERATION?: If it's not a cast spell of first level or higher then the healing power does not trigger the conduit per the language of the power.
My two cents on how it works!