He was. I really wanted to hack at his face with a chainsaw by the end of Naruto.
In answer to your questions:
1) Kakashi is their sensei. When the three first graduated from the ninja academy at the beginning of Naruto, the three were put in a squad and assigned a higher ranking ninja to be their sensei. Kakashi's a special Jonin, nicknamed 'Copy Ninja' or 'Sharingan Kakashi' because his left eye contains the Sharingan, a special eye jutsu that usually only belongs to the Uchiha clan. But I can't tell you how he got it, that'll give it away.
2) Gaara is the younger brother of Kankuro and Temari, and the current Kazekage of the Hidden sand village. He had one of the 9 tailed beasts, the one tailed shukaku, sealed inside of him at birth, which protects him by manipulating the sand he carries around in the gourd. This sand moves of it's own will, and it doesn't allow any harm to come to Gaara, even self inflicted. He can infuse his chakra into the sand to perform more powerful jutsu.
3) I suppose in a way he is special, each ninja has their own unique battling styles. For example, Shikamaru uses Shadows, Gaara uses sand, and Kankuro uses his puppets. However, there is another puppet user out there, but I cannot elaborate or I'll give the plot away.
4) Not everyone wants to kill Gaara. The criminal organization, Akatsuki, want him so they can extract the Shukaku from his body and use it's power to take control over the world. (There is another motive, but I can't go into it)
5) It's not never ending. There's just a lot of it in there. This is so if he is battling in say, a forest, he still has sand to use, because otherwise he'd be defenceless as using sand is his main battling style.
6) His face isn't falling off, what is falling off is a layer of sand, known as his sand armour, that he maintains using his chakra. Seeing as he's been knocked out, he can't control where the chakra goes, meaning the armour will slowly weaken until it is just normal sand.
Wow that took longer than expected. Hope that helps.