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So I have a minecraft rig that uses one IK bone for the arm.

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What I want is for the bone to move up when the controller moves up as well, and when it goes down, for the IK bone to not go below its limits.

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As you can see, moving the controller up and down doesn't currently affect the IK bone.

enter image description here

What I want is something like this, but when the controller moves. Also, I want the arm to return to position if the controller is moved forwards or sideways and for the IK to continue to be parented to the torso bone.

I hope this is clear enough of what I want. I definitely know in my head how I want the bone to act, and I feel like it is possible inside of Blender, but I've been messing around with the bones for a while now and I still can't figure it out.

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The IK goal is to manage a chain of bones and bend them from point A to point B with an orientation towards point C. Here you have just one bone, you should use a damped track constraint instead, which has the simple role of pointing a bone towards another and seem to be what you need.

Then, before the damping track, you can add a Child of with only Z translation enabled. Don't forget to hit the set inverse button.

demo gif

You still need to add Copy Rotation on the constrained Bone, Target:Armature Bone:Bone.001 so that it would follow the rotation on Target:Local Space, Owner:Local Space, Axis: only Y. if not Target:World Space Owner:World Space, Axis: only Z

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