I think that Dumbledore was terminally ill after trying to destroy the horcrux ring, hence the shrivelled hand that just won’t heal. and he and Snape are the only ones aware of this, hence Dumbledore’s change in tactics and haste in making harry aware of his research efforts so far (so that he is prepared to carry on later).
am convinced that Snape is on the side of the light and hasn’t turned. I believe he made the unbreakable vow to Narcissa as he was trying to turn Draco, then told Dumbledore about this. so he was staying intentionally ambiguous on his way to the fighting until he reached the top of the astronomy tower when confronted with a clearly dying Dumbledore and more DE’s than he can feasibly take on. then he and Dumbledore had a bit of a conversation via legitimacy that was Dumbledore urging him to kill him (he was done for anyway and by doing this Snape can fulfil his vow and obtain further favour with Voldemort). after all, if Dumbledore can give similar orders to harry on the way to the cave, why can’t they apply to Snape? I think this is supported by the fact that Snape tries in his own way to protect both harry and Draco when he is making his escape. a duelling champion such as he could easily have overpowered harry at the time. he even encourages harry to continue with occlumency training (if in his own sarcastic way).