Hi Vetetio! Thanks for the comments. You're right, some of the interactions at the table are quite convoluted and explaining them in written form isn't super easy; we certainly want to provide a summary of the rules and many more examples in future version. As it is, we were already over the word limit so we weren't able to, unfortunately.
You're spot on in thinking about flashbacks in a movie! We wanted the feeling you get in a LeCarré novel of slowly piecing things together and figuring out what really happened.
There isn't a "conflict mechanic" per se: you just need to have a card in your hand, and play it. Any card will do, and there's no comparing card for higher numbers. Cards are just a way to keep track of resources: you get resources by adding something to the story (through approaching or revealing a relationship), then you spend those resources to make a different contribution that has a big, lasting impact (acting or revealing other secrets).
Glad you like the epilogues! It's heavily inspired by one of our favorite games, Psi*Run, but the finer points of how it's implemented here (like the reverse turn order) are Flavio's doing :)