1.The BCDC would hook to the factory positive (which is connected to the cranking battery) and use the same ground it uses now.
2. Yes and No. Check the Q&A for the full answer:
https://www.genesisoffroad.com/gen3-jt-dual-battery-kit#tab-5
3. As long as the two batteries match chemistry, they can be used together. If the cranking battery is AGM, the only requirement (aside from being a BCI Group 25) for the second battery is that it be AGM as well.