I finally figured it out how to get resin, but it was a nightmare and a half due to a server lack of information and frustrating mechanics.
I'm assuming you were able to find the tree, which is here
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. You need to hit spacebar to advance the "Found it!" dialogue and enable a yellow up arrow so you can climb it. However, rats seem to be chucking stones at you. The only way to avoid being forced off the tree and to throw coconuts at them by pressing spacebar and using the arrow keys to guide the coconut to the rats on screen. If you clear the screen of rats, the rest of the limited time in the tree will be used to collect the resin. Once you're off the tree, regardless on if you're forced off it or not, you'll have to come back tomorrow to try again.
As for the resource gathering like the coconuts, you can just click them; but they do seem to spawn at random and can despawn if you're not careful.