(I am not a geologist:) From what I understand, burying wood stopped being particularly effective a few hundred million years ago at the end of the carboniferous era. Before then, plants were producing tons of lignin, which few fungi or bacteria were able to break down. Most coal comes from carbon sequestered in this era. Peat bogs seem to be an exception to this; certainly there are still some scenarios/environments where burying wood will sequester the carbon. Maybe conditions like that could be artificially engineered in other locations.

You are correct! (as far as I know)