Tree planting is useful if you've built something and demolished it or planted a crop and then removed it - you're left with empty ground where you can re-plant trees that were lost. But, the trees need a decent amount of space between them and other trees/structures/crops, so you won't be able to place any on the starting island at first.
This is a bug that only occurs in the latest version of chrome (older versions work fine). I've submitted a bug report, who knows if they'll fix it. For now, try another browser (firefox is good).
Just to say, even though one of these comments say how to beat the game, they forgot something in the beginning:
If you do medic-patients x2 and then go to the bar, then you can get extra morale before going back to medic
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 "Gragyriss, Captor of Princesses"){kind=icon}
 "Paladog"){kind=icon}
 "Fade"){kind=icon}
 "Globetrotter XL"){kind=icon}
 "Arachnophilia"){kind=icon}
 "Code Red"){kind=icon}
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 "Aground"){kind=icon}
 "Millika Village"){kind=icon}
Tree planting is useful if you've built something and demolished it or planted a crop and then removed it - you're left with empty ground where you can re-plant trees that were lost. But, the trees need a decent amount of space between them and other trees/structures/crops, so you won't be able to place any on the starting island at first.