Precise.
In what context: harder as in metals, or harder as in difficult?
The opposite of "easier" is "harder."
always get harder
Hard
Try harder can be the other way to replace work harder, too.
in what context it is harder than stone = katai its harder homework = moto musukashii
Im gonna guess and say occur.
I will accurate you!
Sometimes; It depends on the context. When you use the word "harder" as for difficulty level, then yes, tougher is a synonym for harder. If you are talking about the firmness of an object, tougher is NOT a synonym for harder. Or if you're talking about the chewyness of something.
Your assertions are not accurate.
accurate
The noun forms for the adjective accurate are accurateness and accuracy.