What is the best nature for Lunala? Its biggest stats are special attack and special defense, so I'm choosing between modest (+sp.atk -attack), mild (+sp.atk -defense) and quiet (+sp.atk -speed).
It's a lot easier to get "perfect" legendary in this generation as you can maximize iv with hyper training. All you have to do is to get suitable nature.
Not unless you want to get perfect Hidden Powers as well. In some builds for Xurkitree, you want HP Ice on it. Best spread would be 31/0/30/31/31/31. After that, you can do Hyper Training to increase its' defense IV to 31
without losing HP Ice. Of course the Attack/Defense IV combo can be something else to grant HP Ice but that's just the most optimal spread before Hyper Training. This of course would use up one very precious (without cheating) Bottle Cap.
You can also get one bottle cap if you turn in 30 of the same color shards to an old man in the castle of Festival Plaza.
Another question - where is everstone in this game? Do some wild pokemon hold it?
Not sure about exactly
when you can get it but you can go to Captain Illma's house to fight him and he'll reward it to you afterwards. IIRC it's to the top-left of the Pokecenter in the main city of Melemele Island. One of the houses on the sides. His pokemon will be around lv 18 or so, so it should be pretty early in the game.
If you guys have CFW, which you probably do if you're playing the game early, you can follow the instructions here (
https://gbatemp.net/threads/new-3ds-only-pokémon-sun-moon-get-magearna-by-qr.448484/) to get yourself a Magearna. Comes with one Bottle Cap attached.