Why aren't non-Mormons allowed in the temple?
Because temples are considered the holiest places on Earth. Most people don't understand that they're restricted from entering the temples, not because the temples are secret, but because they are sacred. After a new temple has been built, but before it is dedicated as a house of the Lord, there is an open house held. Anyone who wants to can enter the temple and see what it's like. But after it's been dedicated, it's too sacred a place for just anyone to enter.
How do you get qualified to enter a temple if you are a Mormon?
You have to be at least 12 years old before you can get your first temple recommend, but most people get their temple recommends when they're a little older. I personally got my temple recommend when I was 13. Temple recommends look like credit cards or driver's licenses. They have your name, your stake and ward, your stake president's signature, your signature, the words "Church of Jesus Christ of Latter Day Saints", and your bishop's signature. You can technically enter the lobby of the temple without a temple recommend, but to get further than that, you need to have your temple recommend. In order to get a temple recommend, you have one-on-one interviews with your bishop and stake president, and if they think you are worthy, you receive your temple recommend and they both sign it. You also sign your temple recommend, signifying that you are promising to remain worthy of the honor. In order to qualify for the interviews for the temple recommend, you must have been a member of the Church for at least one year. You have to renew your temple recommend every two years. It doesn't cost anything to get a temple recommend, or to renew it. You need to renew your temple recommend to ascertain that you are still worthy, because people can change a lot in two years. Someone who was worthy two years ago, might not be worthy now. Also, once you're out of the lobby, you change out of your street clothes into pure white robes. This is purely symbolic. Ordinances performed in temples include baptisms, sealings, endowments, etc. We are not supposed to talk about these ceremonies in detail outside of the temples. Again, this is not because they are secret, but because they are sacred.
Other than what you've already posted about the Word of Wisdom, are there any other restrictions on Mormons like swearing, clothes you can/can't wear, etc.?
We are not supposed to swear, because profanity is considered very disrespectful to ourselves, to the person to whom we are speaking, and to the language itself. We are also technically not supposed to use replacement swear words such as "dang", "heck", etc. because the intent is the same with these as with the more hardcore swearwords, so it is equally disrespectful. However, many Mormons do this anyway. It's very difficult not to, words just slip out. I catch myself doing it sometimes as well.
We are supposed to wear modest clothes in everyday life, and to dress nicely when we attend church. We are not supposed to get any tattoos. Men are not supposed to get piercings; women are allowed a single piercing per ear. It's also an unspoken rule that long, hair is frowned upon in men.
Are there any special holidays for Mormons?
The only one that I can think of is July 24, Pioneer Day. It is also a state holiday celebrated in Utah. We aren't excused from school and we don't have any special celebrations, though. Most Mormons, myself included, just use this holiday as a way to use up any fireworks we have leftover from the 4th of July.