Animal attacks are not unarmed, I believe; they're natural weapons.

Items like the Amulet of Mighty Fists do work with natural weapons according to table top rules, so they should work with your animal companion's attacks. (Same with the Amulet of Agile Fists.)

I've heard that camping supplies are required for the Trickster mythic path summons, though I haven't verified it personally. Aside from that, unless you're actually playing Kingmaker (as opposed to Wrath of the Righteous), I believe they serve no purpose. (Assuming you're talking about the inventory item.)

I think the camping supplies can be used by the appointed cook during a long rest to provide special buffs.

At least in Kingmaker, camping supplies and cooking ingredients were completely separate - camping supplies were 10 pounds each, and you'd either need 1 per companion each rest (animals don't count) or spend time hunting with a lore nature check. Whereas cooking worked exactly the same as here in Wrath, a thing you'd do *while* resting that would consume a different set of (lightweight) items and give various small buffs.

TL;DR, camping supples are only a thing in Kingmaker. There *might* be a dummied out supplies item still in the game code, but they're not necessary for resting. There's even a loading screen tip that says they're not required here.

As for the trickster path stuff, I can't confirm that either, though it's possible they may use something like the alcohol clutter items as consumables, similar to how other spells like stoneskin or raise dead consume diamond dust, diamonds, or some other item with each casting.

The one case of a Trickster ability requiring a material component that I am aware of is one particular spell that requires some gold coins. I believe you used to need 25 of the Gold Coin item to cast that spell, but getting that was impossible because this particular item doesn't enter your inventory if you do pick it up (it instead gets added to the amount of money you have); a patch (post 1.2, but before 1.3) made the spell cost money instead, so it can actually be cast.

Not actually sure about Trickster summons, however.

thanx for the help.