1) The production guild would obviously be concerned with the resources used for production as with what we know having it become known someone can produce resources for construction projects the way that Miyabi did could impact almost all other production outfits.
They can be concerned, but that doesn't give them any right or control over it. Same as you having an Italian restaurant can be concerned about someone else starting up an Italian restaurant on the other side of the street.
If Miyabi uses his own resources, obtained by him legally, then that's that. The guilds only concern they can act upon is whether those resources were obtained legally. It's as simple as that.
2) This project of his is pretty ambitious from everyone else's point of view and would need to be authorized by the Duke at the very least because it's the Duke's land.
Which is exactly what I said. I literally wrote that the only one in this whole discussion that has any actual right to discuss anythin here is the Duke due to owning the land.
The terraforming that is suggested would also impact the resources available to the Production Guild (...)
Again, doesn't give him the right to be anything more than 'concerned'. Once again, Miyabi intended to use his own resources. As long as those would be sourced legally (him gathering them himself, buying them from the market etc.) then the guild can do nothing but twiddle their thumbs. By no means does it give them the right to interfere in whether this would be made or not.
As far as the legal management of access to certain resources (like mines) goes...again...it's the Dukes land and his approval or denial is the only one that matters.
(...) and even if it's just him and his friends, as well as would impact merchants with the issue of how does that impact merchant carts and adventurers with adventurers are paid to protect carts for days.
Same as above. Nothing you said explains why they should feel entitled to have more say and more control over this project than Miyabi, on par with the Duke. You just completely missed the point of everything I wrote.
3) The merchant and production guild leaders are dealing with someone who seems to be an upstart from their perspective, whose proposal would heavily impact both of their guilds interests. The production guild leader is also just someone who clearly thinks of commoners and probably non-humans as beneath him.
And? How is being an idiot an excuse for idiocy? If you're not trying to excuse their idiocy, then what is your point with this part?
4) The Duke has to figure out how to balance all the guilds and its more important not to overly antagonize them then Miyabi.
That's not true at all. For starters, the Duke even made them aware at this point. He had no reason to. If they weren't aware of it at the negotiation stage, they couldn't even 'show concerns'.
Also, you seem to misunderstand the kind of power that a Duke has over their land in such settings (like in medieval Europe). The guilds work because the Duke is allowing them to. They have any authority because the Duke offers it to them. He could throw out these guys and take over the guilds if he so pleased. It's non-sensical to believe that he'd have any problems due to that as long as his management over the people under these guilds (the average Joe or Jane merchant, craftsman etc.) would work well.
You did watch/read too many stories with adventurers guilds being these super-powerful cross-border entities, and you lost sight of how these things ACTUALLY work. It's plainly shown that this manga is leaning more towards how it WOULD work in real life. Proof? This very story arcs existence. If Adventurers guilds were that global entity, there wouldn't even be any need for the train in the first place. And we're talking about two towns in the SAME kingdom.
The guilds are local and they are made and controlled by the landlord. Duke in this case. That's a fact and it means that all of them are just nothing more than 'managers' of specific parts of the Dukes businesses. THEY (as individuals) have zero authority. As representatives of the guilds under the Duke, they have only as much 'authority' as he permits them. Meaning...if they go against him they have exactly zero if it.