In some interviews and previews, Bethesda said some vague words about town economies and how you could help them by using the lumber mills etc.
But, what is the point? I mean.... You can for instance sit there and haul logs onto the saw forever, and the cut log will disappear into the pile of already cut logs.
But is there any actual coding that ties it into anything? Will the merchants in that town have more gold to buy stuff next time their stock respawns, or anything else?

I mean, if they took the time to add those animations and let the player do it, it has to have SOME tiny miniscule function at least, right?
Same question regarding the small villages you can find in the world, where you can harvest their crops and sell it back to them "honest work for honest pay".
Will it like, improve their economy a tiny bit by having it harvested faster, or does it serve no purpose what so ever other than letting you earn 5g? (which seems pointless)

Not sure if it ties into game play at this point, likely - no. Maybe it will in the future. Many RPG's implement useless interactions like this to help roleplayers who wish to live fluidly in the world. For example, the Gothic series - those game arguably had more useless RPG interactions than gameplay itself.

I enjoy them, they don't harm anything.

I think it is mostly to satiafy RP needs.

I've only read that you can sabotage the lumber mill and cause arrows to increase in price due to wood shortage.

But I don't know if you can help the lumber mill and cause arrows to LOWER in price. I think you can only affect the economy in one way, negatively.

That wouldn't make any sense. If you raise the price its good for selling,if you lower it its good for buying.

Lol i should do some tests, kill the lumbermill workers then press T and wait like 10 days, see if anything changes in the stores.
Then again, tedious.. Won't bother