yes it will come back if you defeat the E4 and Lance. It will keep being that until you catch them. Same rules apply to other legendarys
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I haven't found any reliable sources, but I believe Raikou, Entei, and Suicune all come back after the Elite Four if you didn't already catch them.
no
You would better hope u saved the game.because after u faint cobalion, the Pokemon will never come back. That was your last chance
Yes, Azelf will respawn, if you have fled or accidentally faint it, after defeating the Pokemon League.
No. If you haven't saved since then restart and try again, otherwise you missed your shot.