Yes, this is a very common pursue/distance dynamic in troubled relationships. For many years my H pursued me & the ways he pursued me pushed me further away. Then he gave up & stopped caring so much. Then the affair. And now I struggle with the pursuing role. It is very tricky to get out of, I think.
So do you feel reassured that he is not who the OW is engaged to? I hope so. That is a definite panic moment.
As far as doing stuff together... are you at all interested in what he is doing w/ his friends or is it an all guy thing? I'd say you guys definitely need to find some fun for the both of you in order to put some enjoyment back into the relationship.
T: 14 M: 12 D: 9 S: 6 BD: 2/18/15 (H affair) Working on marriage: 3/12/15-6/11/15 Broken Trust (my error): 6/11/15 H ring off: 7/6/15; Comm w/ OW confirmed 7/13/15 H wants to work on fixing things: 7/21/15