Even if the wood is cut down and used for lumber, the lumber stores the carbon for a very long time. And as you point out, while trees do in fact die and rot --- it's also true that new growth is always happening. Forest are great carbon sinks --- not that it matters because CO2 does NOT drive warming.
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A carbon sink would be a place that would store excess carbon. A forest might increase in mass somewhat but it essentially gives off as much carbon as it takes in over a long period. For me a forest isn't much of a sink. The trees take up carbon from the atmosphere only to release the leaves later and in the process of decay or digestion they return that carbon to the atmosphere. The actual biomass can change somewhat depending on conditions but once it reaches a certain stage it essentially becomes carbon neutral. An exception would be when the plant litter builds up as it does in a bog.
I think you may be missing my point. For something to really be a sink, it has to take up additional carbon. The ocean does this by absorbing carbon from the atmosphere in one place and depositing in other places as sediment from chemical precipitation or through precipitation or accumulation of biological remains.
An oil reservoir can be thought of as a dam in a river. The trap (reservoir) will fill and when it does the rest goes over the spill way. In this case the spillway is upwards to the surface. Much of it turns to CO2 on the way up as it is oxidized.
If the tree can live a thousand years, there should already be trees a thousand years old in the forest. Anyway, what is a thousand years to a geologist but a mere second in geological time.
Depends on the size of the forest. But, yes, that's one of the reasons that deforestation is a contributing factor for AGW. If we decrease the amount of the Earth's surface that's covered in forest, we decrease the natural stores of non-atmospheric biological carbon, which increases atmospheric CO2.
All of it.
Remember it's not just the wood, it is also underground biomass (root systems) the top soil, and the leave litter.
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