The text doesn't say "other" target creature, or specify a creature I contol or an opponent controls, so I assume that it is perfectly legal to cast Hunt Down and choose one of own creatures as both of the targets for this spell? (Even though it really makes no sense!)
Correct. Because there are multiple instances of the word 'target' you can target the same creature twice. Here is the relevant rule
601.2c The player announces his or her choice of an appropriate player, object, or zone for each target the spell requires. A spell may require some targets only if an alternative or additional cost (such as a buyback or kicker cost), or a particular mode, was chosen for it; otherwise, the spell is cast as though it did not require those targets. If the spell has a variable number of targets, the player announces how many targets he or she will choose before he or she announces those targets. In some cases, the number of targets will be defined by the spell’s text. Once the number of targets the spell has is determined, that number doesn’t change, even if the information used to determine the number of targets does. The same target can’t be chosen multiple times for any one instance of the word “target” on the spell. However, if the spell uses the word “target” in multiple places, the same object, player, or zone can be chosen once for each instance of the word “target” (as long as it fits the targeting criteria). If any effects say that an object or player must be chosen as a target, the player chooses targets so that he or she obeys the maximum possible number of such effects without violating any rules or effects that say that an object or player can’t be chosen as a target. The chosen players, objects, and/or zones each become a target of that spell. (Any abilities that trigger when those players, objects, and/or zones become the target of a spell trigger at this point; they’ll wait to be put on the stack until the spell has finished being cast.)
As a bit of clarification, if the creature targeted to block can't block the first target, nothing happens. So, while you can target the same creature for both instances of the word target, it won't actually result in the creature becoming blocked (or blocking).
...So, while you can target the same creature for both instances of the word target, it won't actually result in the creature becoming blocked (or blocking).
Right. I want to cast thus on my Sage of Hours, to give him two +1/+1 counters. Will that work? Or will he only get 1 counter because it's only 1 spell?
601.2c The player announces his or her choice of an appropriate player, object, or zone for each target the spell requires. A spell may require some targets only if an alternative or additional cost (such as a buyback or kicker cost), or a particular mode, was chosen for it; otherwise, the spell is cast as though it did not require those targets. If the spell has a variable number of targets, the player announces how many targets he or she will choose before he or she announces those targets. In some cases, the number of targets will be defined by the spell’s text. Once the number of targets the spell has is determined, that number doesn’t change, even if the information used to determine the number of targets does. The same target can’t be chosen multiple times for any one instance of the word “target” on the spell. However, if the spell uses the word “target” in multiple places, the same object, player, or zone can be chosen once for each instance of the word “target” (as long as it fits the targeting criteria). If any effects say that an object or player must be chosen as a target, the player chooses targets so that he or she obeys the maximum possible number of such effects without violating any rules or effects that say that an object or player can’t be chosen as a target. The chosen players, objects, and/or zones each become a target of that spell. (Any abilities that trigger when those players, objects, and/or zones become the target of a spell trigger at this point; they’ll wait to be put on the stack until the spell has finished being cast.)
Right. I want to cast thus on my Sage of Hours, to give him two +1/+1 counters. Will that work? Or will he only get 1 counter because it's only 1 spell?