No and no. A hard mattress might be excellent, but only if that's what feels comfortable to you. If you like a softer mattress, your back will be fine. There is such a thing as too hard. There is no scientific consensus on what makes a good mattress.
Comfort depends on a balance of heat, moisture and pressure against points of the body.
Comfort is subjective. Around the world, people sleep comfortably on straw mats or the floor, in hammocks, and on mattresses of every description. This is one category, at least, where what feels good is good. If your mattress has developed peaks and valleys or sags in the center, or if a coil is poking out, or if it's just not comfortable, you need a new one. Mattresses wear out at different rates.