1. I don't know those words, but i do knows of words that are really similar to them from the Kansai region. it would make sense that someone teaching someone else japanese would only teach standard japanese (the one used most in Tokyo). My sister's the huge Kansai freak, but she's not home right now, so... *shrug* they elude me.
2. Pronounced similarly as skee, the 'u' is nearly silent, you can voice it if you want to be extra emphasis on it, but it should be silent. the 'i' part should be read as knee is sounded in English, so basically you get something like skee.
3. Those are all essentially the same word if you put them in English like that, but really they're like 'excuse me' 'i'm sorry' 'pardon me' and so on and so forth. They each have their own usage placements, such as Gomen Nasai is used for a literal, I'm sorry. Then the next will be something like I'm sorry/Excuse, you can go next in line. Situations like that make these words, though similar, quite different.
4. Gah... >_> Reminds me of Beckii Cruel. I don't know why they're clapping or she's laughing. sorry couldn't be much more help on that.