You need fresh water, soap, food and fire. You have sodium metal, salt water, flint rocks, vines, coconuts, "palm" fronds, bamboo trees, gourds and fish.
To get fire, all you need to do is get the sodium wet and ignite some of the plant substances with it. I think salt water will do the job just fine. For the distillation, you could use coconut shells as containers, or even make a roof of palm fronds and boil the salt water underneath. The steam would condense on the palm fronds, run to the edge (you'd make the roof slanted), run to the corner (the edge is also tilted), and drip off...into a coconut shell. Of course the dirty, salty palm fronds wouldn't produce the cleanest "fresh" water at first...
Soap can be made from ashes and animal fat. I read this in one of the Chronicles of Narnia, but I don't know the details. Google it.
Food's easy, since you already are given fish, coconuts etc. I don't know what your teacher wants with respect to the food. Just boil the fish in coconut shells and you have cooked food. Put some of that salt left over from the distillation for flavor if you want.
Why does the fire need to have little smoke? Is that one of the rules? Palm fronds can make smoke; smoke is what you get when the combustion doesn't finish and so doesn't go all the way to CO2 and water, but instead produces tiny particulates of charred plant matter which make up the smoke.
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