If you cast half of a split card (for example, Hit) and reveal another one of those split cards when the ripple ability resolves (for example, Hit // Run), you may cast either half of that split card (Hit or Run) without paying its mana cost.

If you cast a spell that already has ripple (such as Surging Flame, which has ripple 4) while Thrumming Stone is on the battlefield, both ripple abilities will trigger separately. Assuming you choose to do all "you may" actions, when the first instance of ripple resolves, you reveal the top four cards of your library, cast all Surging Flames, and put the rest of the cards on the bottom of your library. Any new Surging Flames are on the stack on top of the other instance of ripple, so they'll resolve next. Each of them also has two instances of ripple, which trigger separately, and the process continues until the ripple abilities don't reveal any Surging Flames.