I think they did kill Summer. In V4C1 Hazel said they dealt with their kind before (talking about silver-eyed-women), so I guess they were talking about Summer, since that is supposably a very rare trait. I know that it still could be someone else, but it would fit nice in the story.
Yeah, it would definitely fit nice in the story if Summer were to have possessed silver eyes and even if she didn't possess the trait it could still be stated to be a genetic trait past family members have been stated to poassessed.
1) He could have given away power so he doesn't have to do everything alone. More people can do more things.
How excatly did he get those powers?
Good point. But the overall question still stands: "Did Ozpin willingly give away his powers or was he forced to do so because of some other reason?"
Ozpin could have trained very hard in the usage of magic and obtained this level of skill that way. Or it could have been gifted to him and Salem through some other means.
I doubt we will find out this answer before this season ends.
2) She could be the winter maiden. But I get more of a Homunculus-Hohemheim vibe from them.
3) My guess is that the gods, whoever they are, gave him the job to stop Salem, but he failed, so they punished him with eternal reincarnation until he can finally finish his promise and then die after that.
2) If it did turn out that Salem was the winter maiden and Ozpin didn't inform his little group about it, then I can understand why they might be a little upset with him later on. So you got a Homunculus-Hohemheim vibe from Salem, that is interesting because I was thinking along the lines of Yuuko from XXXholic or Sarah from Vampire Knight.
3) I hope that this doesn't turn out to be the case. I would like for some personal attachment between Ozpin and Salem to be revealed before defeating her for once and for all. I wouldn't mind if it turned out that Ozpin was the original evil person and Salem was the good person who tried to stop him but due to some unknown events, Salem and Ozpin roles were flipped and Salem is fighting against her fate.