Reading your posts, its clear that you have so much hurt and anger and resentment. This is the hardest thing any of us will ever do. Try to keep your head up as much as you can. I would highly recommend watching the TED talk by Shawn Achor on Happiness. Then take the 21 day challenge. Im sure you'll surprise yourself when you see how many good things there are in this world for you.
As for your questions on giving up and hope, thats really up to you. In my opinion, you have to let him go. Let him live his own life. Truly, drop the rope and let him go free. Not just physically, but emotionally. Stop carrying that weight around. Im not saying to move to a new relationship....Im saying to stop caring what he does right now. Stop worrying about how long he may be with OW, stop worrying about the way he treats his kids, stop worrying about the horrible way he has treated you. Thats all on him. He's in the thick o the infatuation stage - none of the other stuff matters to him right now.
Instead of focusing on him, and on OW, focus on YOU. Are there other GAL things you can do - through meetup groups? through the library? through a craft store? etc. Its time to get your mind off of him and on to you.