Before there was the attempt to send back Wolverine to the past by 50 years, during the battle Professor-X, Scott and Jean was alive, although they should have been dead? Can anyone give an explanation for that? They died at the end of the last X-Men as far as I remember.
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The post-credits scene from X-Men: The Last Stand strongly hints that Professor Xavier survived by planting his consciousness in a comatose man. Wikipedia claims that in the DVD commentary the writers indicate that the man is a twin brother of Charles, explaining why they look exactly alike. I've heard that claim many times, but I don't own the DVD, so I can't check. Whether it's his twin brother-- or whether he had plastic surgery or something all that matters is that the Professor survives.
But I'm afraid you're a bit confused when it comes to Cyclops and Jean. The opening battle contains Shadowcat, Bishop, Blink, Sunspot, and Colossus, but not them. Their only appearances in Days of Future Past occur after Logan creates a new timeline.