1. Is pagan an umbrella term?
Yes and no. Paganism means anything not following Judaism, Christianity or Islam. However I know a few people who call themselves 'Pagan' so you can also.
2. Why are Wiccans Witches?
Ever heard the oh so confusing phrase 'all Wiccans are witches but not all witches are Wiccans?' I'm probably going to mess this whole thing up but Wicca is a religion, but since it has many elements of witchcraft, some Wiccans call themselves witches. Witchcraft is also a religion [which I'm not qualified to explain, ask a Moderator like Brysing] but it has some differences like they don't follow the Rede so they just go by 'Witch'. Think of it like Christianity, an Anglican and a Baptist can both call themselves Christian, it's the little differences that makes them 'Anglican' or 'Baptist'.
3. Because they do rituals and spells?
Not 100% who you mean, but both groups do rituals and spells [and to really confuse you both witches and Wiccans dont always cast spells] I've heard people claim Wicca is the Cathoics of the pagan community because of their rituals. I know both witches and Wiccans who don't cast spells, but all Wiccans I've met preform at least some form of ritual while I know some witches who might acknowledge a Sabbat but won't cast a circle and preform a ceremony/ritual. Again, just subtle differences.
4. What do I call myself?
Anything you like really. I go with Wiccan or Witch, I know people who go with Pagan, I know some who prefer to call themselves a Buddhist because they follow the Buddha's teachings just with some witchcraft elements. Decide for yourself, there really isn't a wrong answer. Just research the history of the word should you choose something like Shaman, Mage or warlock.
5. Is the pentacle Wiccan?
It's an old protection symbol used by many groups from witches to even Christians. If you feel drawn to the symbol use it. It's not the symbol that has power but the power you give it. You believe it has power therefore it does.
6. How long should I study before calling myself pagan?
I know people who started calling themself a witch minutes after reading a Wikipedia article, and I know witches who studied for a year or more. Whatever you're comfortable with. Personally I would hold off until you know the basics of the religion before jumping on board, but it sounds like you've done some leg work already so go for it.