Work on building from the bottom up with your friendship with C. No expectations, one step at a time. Don't rush, you have all the time in the world.
AS for the dates; it's basically up to you. Only you know if you want to keep them going.
I think your X is confused, as my H is. They cheated on us and now they have to forgive themselves. You need to work on forgiving her too. I know when I wrote that letter to my H; I meant every word. I'm working on forgiving him as I now understand the whys of the A.
So set yourself free of the burden, forgive C for the A. they were lacking something, it doesn't mean they are a horrible monster. They are just human. I'm not saying that an A is OK, I'm saying I understand why my H fell. I'm willing to brush off the dirt and rebuild a new R!
I have no idea if my H is still having an A. Sometimes they can't seem to make that step; to let go of something that made them feel alive, even if it was short-lived!
Many positives and a few baby steps; keep up the friendship!