It's left up to the viewer to decide for him or herself basically. There's no definitive answer as to whether they did or not, but my personal take on is that it's a bit of a test of faith, and that you have to believe they survived. It wouldn't make a lot of sense if they didn't really, seeing as the whole point of the ending was that it was making Robin out to be the hope for the future of witches. Besides that though, there's Dojima's comment about how there's no way they could have made it out, and Karasuma's response to her that it must have been some kind of miracle. That makes it seem pretty clear to me that they know that they made it out alive, but that they've decided to act like they didn't and tell that story of them being dead so that Solomon will have no reason to continue hunting for them.
As to who that new mystery hunter is that shows up at the STNJ's doorstep in the final scene, there's no way to know, but after all that happened I don't really think I can see Robin coming back to hunt for them again like she did before, but there's always the possibility I suppose that her and Amon could have made some kind of reconcilliation with Solomon HQ that would have allowed them to return to work there somehow. If she did, then I imagine the aim of the STNJ would have to change a bit, and that it would move away from simply hunting down witches and more towards helping them learn to control their powers and become more responsible and productive members of society.
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