I'm not stating I'm an expert on the fine details of what you are asking, just going off of what my interpretations of the regs are. If you're doing something that is serious you should go to someone like Dave Dunbar who can guide you through those details. Those Regulations are here: https://www.ttb.gov/spirits/bam/chapter4.pdf
1. Yes, that would be the Distilled Gin. "DISTILLED GIN: Gin produced by original distillation from mash with or over juniper berries and other aromatics or their extracts, essences or flavors"
2. Redistillation - flavoring GNS or other spirits with botanicals.
3. Mixed question here - if you're redistilling after maceration then it's Redistilled gin and doesn't need GNS, it can be any spirit. If you don't redistill then it's compounded gin that does require GNS.
REDISTILLED GIN: Gin produced by redistillation of distilled spirits with or over juniper berries and other aromatics or their extracts, essences or flavors
COMPOUNDED GIN: Gin produced by mixing neutral spirits with juniper berries and other aromatics or their extracts, essences or flavors
4. The regulations do not state what type of still is required so any can be used.
5. The still type doesn't matter. If you use a pre-distilled spirit it's redistilled Gin.
6. See 5.
Again - there's way more to this than what is above. Dave can guide you through it.