For etching runes onto something, which specialty crafting applies (if any), and which set of artison's tools are needed?
Is it based on what you're etching them onto (so often Blacksmithing, Leatherworking, woodworking) for metal armors/weapons, leather armors, wooden weapons?
Is it 'Artistry' as its sorta like fine-art, engraving onto something?
Yes the feat is needed. You still need tools for any crafting to avoid a penalty. You can also get a bonus from specialty crafting, even for some magical items.
For etching runes onto something, which specialty crafting applies (if any), and which set of artison's tools are needed?
Is it based on what you're etching them onto (so often Blacksmithing, Leatherworking, woodworking) for metal armors/weapons, leather armors, wooden weapons?
Is it 'Artistry' as its sorta like fine-art, engraving onto something?
I'd say it's based off of the item you're making. My reasoning behind it is that once the rune is applied to the item, it's now a part of the item, meaning the tools must be reasonably applicable to the item for the rune to work. In addition, you need the relevant tools to effectively apply the rune. Using woodworker tools on full plate, for example, are probably not very effective and would probably not work. For transferring from a Runestone, not only would you need Stonemasonry, which works with stone goods (of which a Runestone definitely is), but you would also need the artisan craft relevant to the item you're etching the rune into, such as Blacksmithing for metal armor and weapons, Woodworking for wooden weapons, Tailoring for cloth/leather armor and items, and so on.
Additionally, Artisan's Tools are listed to be specific similar to the Specialty Crafting feat. So, you can have Stonemasonry Artisan Tools, but those are different from Blacksmith Artisan Tools, and so on. Needless to say, you'll be glad you have all those Bags of Holding to hold all these annoying Sterling Artisan Tools.
Well bag of holding with all the cheap artisan's tools + a single crafter's eyepiece is the cheaper solution I think if you're an omni crafter. Item bonus from the crafter's, and regular tools to avoid the penalty.
I'd go with Artistry or Stonemasonry, given that Runes seem to be ornate designs stored in stones.
Artistry includes jewelry, and engraving leather or metal would certainly fall into that category.
If you are already an magical crafter and have a specialty which aligns with the creation of weapons/armor you most likely already have the neccessary skills and tools for the process
adding runes to a metal weapon is still metalworking - it is probably a different process then the actual forging but you can probably in most cases just use the same tools on the same weapons (even actual etching, if you want to go that way, is just part of the usual process - and a process that was not that uncommonly used to improve the optic of items)
and for engraving metal/stone/leather, it is the same process as the hero probably already uses for other decorations
and wood is even easier
so, if you got a set of artisan tools for your specific prophiciency you are already set
any special short-time tools or consumable items that are part of the process are part of the creation cost of the runes