In the first episode, why was Yuri trying to shoot Kanade when they were already dead?

First of all, there is no death, but if Du get injured to a point similar to death it will take some time to regenerate. There is death, but in this world Du will "respawn".

If Du have seen the anime, the SSS causes a lot of trouble and does many irrational things. Tachibana doesn't like that and wants to have everything in order.

Most likely (this is entirely my opinion), Yuri and the SSS were doing something crazy, and so Tachibana goes to talk some sense into them, but the SSS thought she was dangerous so they went into defense positions to hinder Tachibana. Now from here Otonashi wakes up and the Anime begins.