Part 3: UPDATE 3
Archive 09 - Tamon Takeuchi's faculty ID
Looks like he was born on Valentine's Day, 1969, making him 34 years old in 2003. The game takes place in August, by the way.
Archive 10 - Fragment of megalith
Note that the large Mana Stone from which this chunk was broken off is where Kyoya witnessed the girl smashing something and the ceremony taking place in the first two videos.
Archive 11 - Idol found at bottom of well
Shades of Urashima Taro.
Turtles are common in Japanese folklore, usually with positive connotations, and symbolizing longevity or good luck. Like the fox or the tanuki, they're said to have magic powers and even to be able to transform. The patterns of their shells are often said to be symbols or messages from the gods.