I think the Earth must have slipped into a dream universe where physics doesn't apply. In particular, even if this object is somehow "practically massless", since it is enormous and indestructible and embedded deep in the planet, in a universe with semi-normal physics, it matters how heavy it is, and whether or not it interacts with gravity at all. In any case, I don't really see any possible answers to such questions, which would result in it continuing to stay in place relative to the spinning, orbiting Earth. It will either sink in or pull out, and it will also twist, causing ridiculously enormous earthquakes and magma eruptions, which as others have pointed out, would also have almost certainly destroyed all life on Earth. Even if something survived the earthquakes and vulcanism caused by the insertion, even less will survive when the thing rips sideways through the crust, and/or out the far side.
So... the good news is, you're in a dream dimension or comic book or anime or something, which is ignoring physics and making it stay like that, for now.
Even if the mass replaced by the spear when it inserted somehow vanished, it will now have some pretty interesting weather effects around it, as the atmosphere will flow around it.
Politics? Ownership? Well that's all speculative. Probably there would be many hypotheses about the aliens and why they put it there. "Hey, let's make it into a space elevator and profit" might eventually be a conclusion after nothing else weird happened for a long time, though there might be another popular point of view saying, "hey, let's not mess with it as clearly the aliens who put it there might not like that, it defies all physics, and who knows what the heck will happen if we do that?" Maybe people would use its African location as an excuse to keep it neutral and not allow anyone to unilaterally seize access. Maybe the local nations would try to get the best bids they could. Realistically, Earth politics has become a puppet act of a group of corporations who own most of the world's wealth and bought officials anyway, though, so any such story would really likely be invented by or actually controlled by such organizations anyway. Perhaps they'd decide to capitalize on space, and develop a new giant industrial complex around the site.
But since we've already proven this must be dream universe, really anything is possible.