How can you reuse the wooden spoon?
If you have enough wooden spoons, you could get a geothermal energy generator, hook it up to a furnace incinerator and burn the spoons and get energy from that.
No, unfortunately. Half the weight of the spoon is carbon, and this will be released into the atmosphere when the wood rots in landfill. If you keep the spoon hanging on your wall for years it will store the carbon. If there is another tree growing in place of your wooden spoon tree then your spoon is part of the natural balanced carbon cycle of the earth and you can sleep soundly tonight.