2. The boundary and what it does is stll one of the big mysteries of BB. Presumably it is a 'meta Dimension' that can be accessed through a cauldron (which is a door way into the boundary) The boundary has no sense of time, it is limit less in every direction, and because of the cauldrons, all timelines 'meet there' it has peculiar side effects. The boundary seems to house some kind of great power at the cost of detoriating the mind and body of those who dwell in it. In the heart of the boundary is the Azure, which is kind of like a life stream. Its where all the souls go, or so i believe. The Azure is basically the afterlife, kind of like the Buddhist belief of Nirvana. The Prime Feild Devices were made to explore the Boundary, much like how we make probes to explore space. We cant survive in those conditions, so we made machines instead. One of those machines discovered the Azure. Somehow, by coming into contact with the Azure (the lifestream, the source and ending point of all souls) it gained a soul of its own. Even though it was only supposed to be a machine. Hazama hints that after this, the scientists gave more Prime Fields souls by throwing them into the azure, as it gave them power and strength. (in BB souls seem to be VERY powerful, kind of like Blood Magic in fantasy settings, using souls in BB is morally wrong as it requires sacrifice, but is considerably powerful. By getting a soul from the Azure, they seem to be stronger than just normal souls, and being machines, they can manipulate their personal soul energy in ways humans cannot.) The smelting Process is what turns the Prime Field into a weapon. After it has its soul, its emotions are canceled out in the smelting process, they are turned completely obedient, and they are given/create weapons that interface with their tech so that they can make the most use of their soul (azure) energy. Of course, the weaponized form of a prime field is known as a Murakumo.
The Azure Grimoire/Blaz Blue, is a 'portable cauldron' that I believe has direct access to the Azure. I am confident that what it does is pull soul energy out of the Azure through the cauldron, and through that aids the weilder. At the same time it has an inverse effect, as it also sucks in the soul energy of those around the Azure Grimoire. This is why Ragna and his enemies lose life, their soul energy is being absorbed by the Azure Grimoire, while ragna pulls soul energy directly out of the Azure itself to aid him.
This is my understanding of it.
I may not have described as well as I meant to, just ask me to clarify something and I will.