I want to know if on the second day of Sukkot and on Shemini Atzeret it is off-limits on Yom Tov and that includes switching on or off electrical appliances, driving a car, going to work, handling money and writing. The major differences between the two are cooking and baking, lighting a fire from a pre-existing flame, and carrying in the public domain? Can I rip paper or cut a plastic soda water bottle on these days as will including the first day of Sukkot and Simchat Torah? Do these rules all apply for Sabbath?
The second day of Succos, Shmini Atzeres and Simchas Torah all are considered Yom Tov and have basically the same halachos as the first day of yom tov. We are allowed to bake and cook, on Yom Tov from a preexisting flame etc, carry outside when it is needed for Yom Tov, but not on Shabbos or yom tov that is on Shabbos. Opening a soda bottle on Yom tov will have the same rules as shabbos. A wrapper can be ripped in a way that ruins it, order to access the food inside it, just be careful not to rip letters, words or a meaningful picture.
As a side point it would a good idea for you to get the sefer The Laws of Yom Tov by Rabbi Simcha Bunim Cohen (published by Artscroll). You will be able to read all of the halachos over there.
Have a good Yom Tov