Hello Fernando. I like your new acquisitions. Both are very rustic, but have enormous character. I see no reason why they wouldn't date to 18th or early 19th c. in construction and aging. The shafts have nice patina. I'm wondering if these might be Spanish colonial (again!), only because of their 'construction under extreme conditions' i.e. rough blacksmith qualities. They could, of course, be crude hunting implements, but most of what we see coming from the big countries, especially in hunting, is usually much more upper scale. I'll give you my opinion, as weak as it may be, based on guess-work and deductive reasoning.
The item that looks like a lance is too small to be a lance. Moving on. It is too short and not strong enough to be a military pike. If it is a spear, it is poorly made and couldn't be thrown far. So...
I think your pointed object is either a trench spear (popular in Spanish colonial regions and in the Americas) or it is a primitive boarding pike.
As you know, boarding pikes were much smaller than their battlefield equivalents, ranged from well-made to put-together items stored in large groups, and were just basically pointy sticks to stab boarders with as they clambered over the side. Early pikes, pre-1800, had leaf-shaped or diamond-shaped points, much like yours. You can see similar in Gilkerson, as well as Neuman's.
If we propose that the item is a boarding pike and that the other piece, with its similar age/construction/socket, etc, are a pair, than the other hook piece is probably a gaff. You can do a search for early ship's tools and see colonial-period gaffs resembling your hook almost exactly. I recently saw a well-documented one which had two hooks on either side and a center spike, almost like an early spontoon. It had the primitive socket and about a foot of old shaft left on it. I was surprised how poorly cut the wood pole was, being warped and rather thin. It had supposedly come from a wreck at the North Carolina coast (the Graveyard of the Atlantic, as they like to call it).
Anyway, it does fir the description. Of course, you know me! I see something 'nautical' in everything I look at-
Mark