Lost in Blue

#16: Flat Fish - Ocean (rare); #17: Sea Bream - Ocean (rare); # 18: Parrot Fish - Ocean (rare); #20: Cat Fish - Stream in the grasslands; #22: Arowana - Stream in the grasslands (rare); #26: Stream in the grasslands (rare); #26: Japanese Huchen - Stream in the grasslands (rare). You need to use the rod to catch these fish.

Is there an option for asking Skye to fix you a lunch box? I simply don't remember.

You can find the beautiful stone along the trail/maze north of the second cave where the poisonous gasses are. It was near the beginning of the trail. Have your backpack full and walk around pushing the A button (like when you are collecting spices) until Jack says "My backpack is full." Then toss an item and dig in that spot.

Lunch box?
If I didn't remember wrong,
you have to play as Skye to make one.

You can't get a lunch box playing as Keith, only when you play as Skye.

Arowana aren't all that rare. You just need to fish in the right place. Go to the base of the first waterfall next to the stepping stones and fish there. Save, but it should usually be one of the first you catch. Sometimes you don't, though, then you just have to reload.

Japanese Huchen are the same, only you need to fish for one at the very top of the map in the grasslands next to the waterfall there.

As for the others, I played as Skye and sent Keith out for food a lot. Eventually he brought me almost every fish I couldn't catch.