1. So, what is this type all about?
The idea behind this type is to partition Grass-type. This part references Grass-type's formerly Special status and implied weakness.
2.Where does this name come from?
The name comes from move Wood Hammer, which has been given a variety of Grass-types. Japanese name of Horn Leech is Wood Horn as well.
3. Does this type have an in-game source?
Not really. Tree-based species are very varied in Pokémon. Some aren't even Grass-type, like Bonsly-line and Xerneas.
4. What would be the ideas behind such a type?
Largely physical moves and healing moves. Special Wood moves are difficult to conceptualize.
5. What would be the type interactions of such a type?
Similar to Grass, but with more physical orientation. The only major conceptualization of Wood-type was done in Brown and Prism.
6. What would be the distribution of such a type?
Relatively rare. Trees are less common than weed.
7. Future comments:
This type can be a theoretical upgrade to Grass-type for late-game.