Is there a downside to stealing from Farmer?
I befriended farmer and got access to his house to take the plot item there. It turns out he has a lot of useful things in that chest, especially that fertilizer.
Can I take the other items? If I do, will there be consequences?
Since the question did not get answered yet and I already saw it on Friday, I will tell you what I suspect.
I don't know any real evidence of any mention of this NPC's possessions.
But the recipe for mead, for example, you get from the private quarters of Horadric the innkeeper. This requires that you make friends with him. Then you can just take it out of the closet and it has no effect on the game except that you have a new recipe.
I think these areas are meant to be a kind of little reward for the effort of making friends with the people, similar to how it is in Stardew Valley. That's why I think you should be able to take the items without any problems.