Freddy killed Joey by drowning him. This was actually a legitimate tactical method, considering he knew from the previous film that Joey had a powerful sonic scream ability which would be useless without the oppertunity to breathe.
That may also account for the window-shattering effect of Alice's scream when Rick is killed. It's conceivable that Kristen didn't just pass on her own powers to Alice, but - thanks to her becoming connected to the boys as Freddy absorbed her soul into the gestalt - Joey's and Kincaid's as well. Alice didn't really know Joey or Kincaid very well, so didn't know enough about them to recognize this or make conscious use of their abilities, but Joey's sonic scream still manifested when Alice was under extreme stress, the same way Joey himself shattered those mirrors.
Alice's victory seems like New Powers as the Plot Demands, especially considering that Freddy's had no trouble with mirrors before. But in a sense, it's just a different application of a power which was already established in Dream Warriors: the ability to draw people into dreams, either one's own or (as implied by Nancy's death) a "beautiful dream" paradise. The only novel twist is that, rather than drawing people from the waking world to a dream, Alice was drawing them out of whatever gestalt captivity-dreamscape Freddy keeps his victims' souls bound within, and into the dreamscape where she was confronting him. Kristen might've been able to do the same, had she only possessed the necessary imagination or insight into how to stretch her abilities.
The 'dog peeing fire on Freddy's grave to resurrect him' is less of a Big-Lipped Alligator Moment when you remember how Freddy was defeated in the last film: last rites being performed on his remains. He probably used Kincaid's dog to desecrate his grave. Or a stray animal took a leak on the burial site in the waking-world junkyard by pure chance, and Freddy incorporated the event (with added pyrotechnics) into Kincaid's dream just to fuck with him.
Freddy needed Alice to pull in new victims. It would seem as if Freddy was holding either the Idiot Ball or Villain Ball for most of the movie by the way he was antagonizing Alice and seemingly intending to kill her. Of course, there are a lot of things Freddy could do to Alice that wouldn't necessarily kill her, but could keep her in a constant dream state with all the victims he could ever want at his disposal. Say, maybe a nicked brain stem or a concussion which could leave Alice comatose...
