All just my own opinions of course.
Put very simply; there is a good ending and there is a bad ending.
The whole of episode five is meant to teach the player that no matter how Max tweaked events she was not going to be able to fix everything, the only thing Max can do is make her choice and live with it. As Dontnod warns at the start of every episode, choices will have consequences.
The five episodes are meant to help Max choose the right choice, to save thousands of lives and Arcadia Bay. To save Chloe and abandon the town, I can't help but feel it is the wrong choice, but its Max's choice to make. Maybe whatever love Chloe and Max have between them will endure the bleak future, but I have my doubts.
Who gave Max her powers and why? Rachel? The Doe? Balthazar? The Silent Hill Gods?
Its pure guess work because its not important to the story, but the best option is the time powers are related to the Native American voodoo suggested through the game, Rachel appearing as her spirit animal the doe suggests they have some supernatural presence in the world.
A gift from the Universe. Without the powers Max and Chloe would have never reconnected in Chloe's final week. The week is an apology from the Universe for handing Chloe such a shitty hand in life, just because it isn't the main timeline doesn't mean it didn't all actually happen. Fate meant Chloe would suffer tragedy and unfortunately this led to her making bad choices in life which eventually lead to her death, something which can't be avoided without terrible consequences. Chloe's final week is an apology from the powers that be, who I believe chose Max because they believed in the end she would set things right and make the right choice. Its also Chloes last chance to do something positive and help counter the Jefferson evil in Arcadia.
The game hints numerous times that her powers are turning her brain into soup, but nothing comes of it. Also, she never runs out of "time juice" again except with that time with Kate, uh?
Running out of time juice is a warning shot from the Universe to tell Max to stop fucking around with the powers, Kate and her fate is a serious warning no matter the outcome and Max does take her powers more seriously from then on. The powers damaging Max is a clear message that she can't change thing.
Does Max still have her powers?
With Chloe dead, the Tornado avoided and the source of evil removed from Arcadia, I doubt, but I bet she will never even try to use them again either way.
In the other ending, yes, and if Max continues to mess with time she will cause an even bigger disaster #darkestimeline
What happens to the various side characters? You can save them during the tornado, but nothing comes out of it.
In the good ending they were never in danger, and as we see at Chloe's funeral they are somehow all brought together, positively.
In the bad ending I don't think any of them get saved, Chloe and Max just make straight for the lighthouse.
What was the cause of the whales/birds/etc dying? The moon? Just Max?
Max, more warnings from the universe to stop.