What happens to Yin and Hei after the ending of season 2? Is it intentionally ambiguous as in they didn't want to commit to a true ending or are they both alive?
Well, Hei is alive, that's for certain; however, what happens to Yin isn't entirely mentioned.

One thing that could prove that Yin is dead is because on near the end of the anime, Yin appears (the one in the white suit) and asks Hei to kill her, in which he agrees. In the OVA, she also says her final goodbye and confesses her feeling for Hei.

However, in the OVA, Izanagi does say that he'll grant Yin's wish which would be to be with Hei, and Izanagi did grant July's wish to be with Suou.

Also, Bai's power allows for molecular manipulation. It is how Hei is a Contractor since she fused with him near the end of Heaven's War and how the plan to destroy all Contractors by destroying Hell's Gate failed and how Heaven's Gate cannot be touched.

At the end, Bai's star which disappeared because Bai was trapped in the Meteor Core began to shine again because she was released. If Hei got Bai's power back, then he could have fused with Yin as well and (if a third season is made) is now trying to find a way to reverse the fusion so that Yin can return to her body (maybe also to allow Bai to come back). However, that is speculation, one thing I've read that while Hei is holding her body, it's glowing, which could mean she's alive, though I didn't actually notice.

I should point out that what we see is a light growing brighter when he puts his hand on Yin at the end. While he could be killing her here, the light could be the same that Hei emitted when he made Anti-Gate Particles nonexistent at the end of the first season.