1. Do the Neo-Reapers have their own barracks and training grounds?
Neo-reapers are just recently graduated shinigami who are given the task of policing the living world and dispatching hollows because the fully-fledged shinigami are busy trying to rebuild Soul Society. As such, they live in the training barracks until they are finally given division assignments.
2. Is it possible for an inner hollow to have a different, more diabolical zanpaku-to?
No. One's inner hollow is a fragment of one's own mind, and would possess the same zanpaku-to as the individual.
3. Seeing as most kido have not yet been shown, is it possible to invent your own, so long as it's reasonable?
Right now, only a handful of characters are strong enough in kido for this to be an issue, but I have no problem with creativity, so long as it's checked with me first.
and while I'm here I'll address a couple other common questions I get:
Is there a list of kido available?
I was going to compose one, but the Bleach Wiki already has a complete list of every skill used and numbered to date, so I simply refer people over to that page.
Is it possible to play as a human, hollow, or Arrancar character?
Currently it is not. I will have blueprints for the creation of human characters with my next rulebook update (version 3) and will continue to develop based on the success of that. For now, new characters are stuck as shinigami. Sucks, I know.
I created my character, how do I go about inserting them into the game?
This one's easy. just write yourself right on in there. If you're really uncomfortable about it, you can request that I write a post that introduces your character, but that's not really necessary. you can literally come right out of thin air and start interacting with people.
My character seems to be ignored, am I not playing right?
well... there's not really a WRONG way to RP, but it's likely you're being too passive. don't settle for writing an introductory post and then waiting for someone to respond. Someone has to take that first step forward in order to make a friendship, and you can't always expect the other person to be the one. Take some initiative and go say hello!