custom block logic - block display

Howdy, just trying to understand custom block logic/block displays
What are the rules for determining which Blocks can be 'custom' blocks or can generate block models. For instance, i think new in town uses droppers as sight planners but they look like crafting tables. 
And  Kawamood's Waystone dp uses heads that have special names when placed use commands to summon barrels and block displays to mask them.
lets say i wanted to have a block like the sea pickle but hang from the ceiling instead. I think i can do this with a block display and rotate it so thats fine.
but lets say i wanted a block to be placed, that is mineable. How can i make one so that when you mine it it keeps it's Name and info?i know can do this with heads. But they don't hang from the ceiling block in a way i like. so i was thinking of trying with small amethyst bud or dripstone.
Is that possible? I might be off base but i think the logic would be. 
generate amethyst with tag, run command that summons display pickle on any amethyst with  tag.
When mining an amythyst with  tag does it go to inventory and keep data? or do you destroy it on mine. But then if destroyed you have to run another command to give an item with the custom tag. And when you place an item with custom tag, summon block display again?