How do gifts work, exactly?

Solution 1:

After playing this game quite a bit, I believe I now possess answers to all of the questions I had:

• There are only two gift items, the Ninjutsu Reference Book available at one of the two item shops and the Flower Bouquet available from Ino's flower shop. The books can be gifted to any of the male characters while the flowers can be gifted to any of the female characters.
• You can indeed give a character the same gift multiple times (as there is only one viable gift for any character) and there is no cooldown.
• Most character do require at least one gift for the maximal friendship level. With the maximal friendship level marked by five heart icons, you can gain one heart for any character by completing a side-mission associated with that character (though some of these show up really late in the game). Once you have one heart for a given character and have unlocked the ability to send letters (this happens once you finish the main plot) that character will then send you a series of three letters for you to answer. A correct answer nets you one extra heart, to a total of three hearts if you get all the responses right. This means that without spending any money on gifts you can go up to four hearts and will need to finish it off with a single gift (though if memory serves, very few characters actually have a pair of missions that make them like you, so you could theoretically not give them any gifts at all)
• All characters have a specific location where they can be found so that you may give them a gift, but as the plot advances some characters might be temporarily absent from their regular spot. Just advance the plot to get them back there (or if they've gone to some other location and are waiting for you to come along so that they can give you a side-mission, go ahead and perform that side-mission).