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.
Go to the y= button, and type in your equation by the y1 (if there's 2 equations, press enter and type the 2nd one in by the y2). Then press graph.
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.
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 "ALPHA", then press "."
Some TI83's can be set up differently, so it is highly recommendable to read the user guide for the TI83 in question. The user would need to go into the VarStat option and enter all the appropriate fields to have the calculator bring in the appropriate variables and totals.
The TI-83 calculator uses 4 AAA batteries.
It will depend on the class. Nothing is impossible without the TI83, but some classes might require it so you can graph and write programs to go along with the math curriculum.
You cannot. A calculator is programmed. It is made to calculate correctly.
http://education.ti.com/educationportal/sites/US/productDetail/us_notefolio_83_84.html
Press MODE and select NORMAL at the top. (You may notice that SCI was selected for scientific notation.)