The material that you read about the "13 powers" is inaccurate and has absolutely nothing to do with Wicca. I note that the whole idea was taken from something written by Silver Ravenwolf who is notoriously inaccurate in the material she publishes in her books.
Wicca and Witchcraft are not the same thing at all. Wicca is a religion with specific beliefs and practices. It has nothing to do with spells although Wiccans do use magic in their rituals. Many, if not most, Wiccans I know rarely if ever cast a spell. You might want to read the article here "What Wicca Is and Isn't" that you can find at http://www.spellsofmagic.com/read_post.html?post=637268 You'll probably want to take some time to research a bit more about the differences between Wicca and Witchcraft before you decide whether these are paths you wish to take.
Since Wicca is a religion one would need to follow the beliefs of that religion and Wicca is specifically polytheistic, in other words believing in more than one God. The traditional deities of Wicca are the Lady of the Moon and the Horned God. There are those who claim to be Christian Wiccans; however, in my opinion they are neither Christian nor Wiccan. You can't sit on the fence. Be one or be the other.
Wicca is not ancient. Wicca was the result of the writings of Gerald Gardner in the 1940's and 1950's. It was once thought that it was ancient but that has long been disproven.
Neither Wiccans nor Witches create storms. We don't have the sort of power that it takes to control the weather; although we may on occasion work with the weather.
There is some truth in the other so-called "powers", but some of the claims are misleading.
Truth be told, you don't have to be a Wiccan or a Witch to do these things and none of them have anything to do with having special powers. With belief, hard work, and study almost anyone can accomplish at least some of them to one degree or another. Witches and Wiccans are not some special and powerful beings, they are humans just like any other.
If you're not interested in a religion, then Wicca probably isn't for you. But if you would like to research it further I'd be happy to point you at some reliable resources.
Or if it's merely the ability to cast spells that interests you I can suggest some great books to read that you might find helpful.
Finally, I would say that when you are living in your parent's house you should honor their feelings and their rules. That only shows your love and respect for them. You have plenty of time to study and practice spells. In the meantime there are lots of things you can learn about such as herbalism, mythology, other religions, history of various cultures, crystals and stones, etc. All of these will be good foundation for your later magical practice.