Not least because said ovens are designed to ignite and burn oil. 
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Only over a 30 to 50 year time scale and even then the large amount of oil burnt in timber extraction and transport means you only regrow less than 50% of the CO2 released. Burning wood is highly inefficient in the shout term, immediate CO2 emissions are very high and even the long term picture is very poor.
Again, this depends.
If you have wood waste (be it from industrial production or from dead wood in forests), the CO2 it emits from burning is te same CO2 it would have emitted when rotting. And the same CO2 it has previously absorbed from the atmosphere.
Of course, cutting healthy trees for this would be crazy and destroy the CO2 neutrality.
Yes but there is an incredible amount of unavoidable waste from forestry. Particularly sawdust mountains near to just about any sawmill.