No. I believe TI83+ and TI84 do use an operating system.
Yes. The TI83 has several applications that can be downloaded onto the TI83, mainly those made by Texas Instruments. Also, you can write your own software.
You don't play as Zelda, you can only play as link. Or in some parts you can play as WolfLink.
Yes. Although I don't know a big list, I am pretty sure that The Legend Of Zelda: Skyward Sword (an up coming Zelda game) is required to have Wii Motion Plus to play.
No, some games require the Wii Motion Plus Remote to play such as The Legend of Zelda Skyward Sword
Play Zelda's Lullaby
you learn it in the game after meeting Zelda
There are online graphing calculators. However, as of writing, there is no emulated TI83 that runs within your browser. On the other hand, if you have a Ti83, it is possible to copy its ROM to run an emulated TI83 on your desktop via one of many emulators.
Zelda is a video game character.
Wii, Wii Remote, Wii Motion Plus, Nunchuck, Skyward Sword, TV
No, it really depends on the college. Some colleges don't allow any calculators for their math classes. Everything that can be done on a TI83 can be done with the human brain, so some professors make tests with easier computations so that you don't have to use a TI83
Press MODE and select NORMAL at the top. (You may notice that SCI was selected for scientific notation.)