There is any relation between strength of the line (for expl. 8-17lb), shown on the rod, and weight that could be lifted by that rod without risk to break it?
Or that numbers related to best casting distance?
There is no direct correlation between the line rating and what the rod can lift. Remember, fish are buoyant in water. When you try to separate them from the water when landing, that is when you are putting the most pressure on a rod. Thus, landing apparatus: net, gaff.
Light, med, heavy, fast, med fast is the “action” or sensitivity of the rod. A lure rating is a guide for casting recommended lure weights for the rod and how the rod will “load up” during casting. For instance, some rods that are more sensitive (light action will have less lifting power than a medium or heavy rated rod of the same rod).
If you are using a rod to lift a fish out the water and up the side of a pier 10 feet or more vertically without a net, make sure you have a rod with the power to lift your targeted fish species.