Welcome to the forum to start with.
Nope, if the effect you want is achieved with 2 coats of oil, stop there, you don't need more. Maybe in months to come, but not immediately anyway.
As for the seepage, that shows you flooded the wood with oil (good technique) and it is the surplus that got into the cracks and fissures that is now draining out. Keep wiping it up, it will stop, but you can also lay on it's side or up[side down as well to help clear the surplus.