Here is the link to the Groovy Bot for the game.
https://github.com/PanAeon/Hearth-Haven-Groovy-Bot
Bot can do a lot of things. I for example brought around 150 logs to the village in just one day without too much pain.
Implemented pathfinding.
Partially implemented farming.
Scripts should reside in scripts directory, and have extension .groovy.
I recommend dissasemble haven.jar, import sources into an IDE, and copy scripts into the project, so you could figure out what API is available.
Based on arksu client, http://code.google.com/p/hh-client/
I don't have much time to answer all questions, and may not answer at all.
For people who don't like bots: Don't use it.
Bot is working you can try it by placing your hearth-fire somewhere in the forest, put a water-flask (full), a bottle-of-wine(full) and a glass into the Inventory (and nothing else), and type ": bot lamber" (Although You'll have to modify it to correctly enter the crate from which bot will eat, and the sign where he puts wood, and the crate where bottle of wine is, and of course place where he will put wood). Bot should find nearest tree, chop it, remove the stump, take log and teleport to your Village, put log to the ground, find nearest sign to the Claim put wood there, find nearest crate, and restore wine in the bottle, and eat from crate near the claim.