Who is that owl? And how does he know everything?
The large owl is called Kaepora Gaebora, and he frequently helps young Link in his quest by providing him with valuable information, and a few times, he transports Link to areas he cannot reach on his own. Although it is only implied in the game by a Gossip Stone, the creators of the series have confirmed that the owl is the same as the character Rauru.Rauru is an ancient sage. According to series' lore, during the Era of Chaos (which came after Legend of Zelda: Skyward Sword), he and the other sages built the Temple of Time over the resting place of the Master Sword, in order to protect the Triforce from people who aggressively sought it. The Temple of Time serves as an entrance to the Sacred Realm, the home of the Triforce. In the heart of the Sacred Realm lies the Temple of Light, which harbors the Triforce. Rauru made sure that the Master Sword could only be reached with the three Spiritual Stones (the Kokiri's Emerald, the Goron's Ruby, and the Zora's Sapphire) and the Ocarina of Time. Pulling the Sword from its pedestal (which only the Hero of Time can do) finally opens the way into the Sacred Realm.One of the rooms in the Temple of Light is the Chamber of the Sages: when young Link pulled the Master Sword from its pedestal, this is the place he ended up, and met Rauru, the Sage of Light. Whenever adult Link finds another one of the other Sages, he returns to the Chamber of the Sages to receive more information from Rauru. In the Child Era, however, Rauru is able to take the form of the owl Kaepora Gaebora from within the Temple of Light, and help young Link in the normal world. When Kaepora turns his head upside down, it looks like a charicature of Rauru's face.Interestingly, Skyward Sword featured a character called Headmaster Gaepora (Zelda's father). Gaepora looks a lot like Rauru, and has thick eyebrows and a triangular beard, just as the owl; he even laughs with an owl-like "hoo-hoo-hoo". He is one of Link's helpful allies by providing information during his quest. It is speculated that Gaepora reincarnated as the Sage Rauru, and hence was also able to take the form of Kaepora Gaebora; just as Link and Zelda always seem to reincarnate throughout the timeline as the Hero and the Princess, Gaepora often resurfaces as the main wise man who helps the Hero on his quest.
Now what exactly is the Triforce, and what happens with it?
Before time began, three Golden Godesses, Din (power), Nayru (wisdom) and Farore (courage), descended towards the land and created Hyrule. When they left for the heavens, they left the Triforce as the basis for Hyrule's providence. The Triforce grants the wish of the one that can claim it, so someone with bad intentions can use it for evil purposes. The Triforce was therefore kept hidden throughout history, in a place called the Sacred Realm. This Realm is said to reflect the nature of the one who can claim the Triforce. As described above, ages before the start of Ocarina of Time, the Temple of Time was built to guard the only remaining entrance to the Sacred Realm, and make sure that only the Hero of Time could enter it.In the beginning of Ocarina, Zelda asked Young Link to find a way to open the entrance to the Sacred Realm; that way, they could prevent the evil Ganondorf from obtaining the Triforce and using it to conquer Hyrule.Link succeeded in opening the door to the Sacred Realm, but Ganondorf secretly followed him into it. The Realm held Link for 7 years until he was old enough to battle evil, leaving Ganon free to claim the Triforce first; it made him the King of Evil, and, mirroring his heart, transformed the Sacred Realm into the Dark World. With his power, Rauru, the Sage of Light, was able to protect the Chamber of the Sages and Link within it from Ganondorf's evil.However, Ganon was deemed unworthy of the entire Triforce, as he only believed in power and his heart was thus unbalanced. As a result, it split in three parts, with Ganondorf keeping the Triforce of Power; the Triforce of Wisdom went to Zelda, and the Triforce of Courage came to Link. In order to obtain the Triforce in its entirety, Ganondorf would have to take the other two parts from Link and Zelda. Zelda and the six other Sages finally succeeded in locking away Ganondorf into the Dark World. However, everyone kept his part of the Triforce, explaining why the Triforce is usually divided over three people in the other games. Ganondorf would use his Triforce of Power to escape the Dark World several times in other games.
What are the differences between the Uncensored First Edition and the Censored Re-Release?
There were three different versions in total. The first one was Version 1.0. The cartridge was golden and common in Japan and the US. A very few copies also made it to Europe. And only that cartridge contains the Uncensored Version 1.0. Then the production was stopped. Two different cartridges in grey were released, Version 1.1 and 1.2. They looked the same and were the most common version, even in Europe. The game was slightly censored but some minor bugs were removed as well. Nowadays, the most common version is Version 1.2.
There's also a GameCube Version, which is actually the censored 1.2 ROM running on a Nintendo 64 emulator. The Wii version for the Virtual Console is also a 1.2 ROM running on an emulator. A detailed comparison between both versions can be found here.