2 questions

this may not be correct, as it's only my take on the film, but I believe Mark has the altercation/bloody finale with the police because in his mind it's the most dramatic way to push a resolution with Anna - to either win her heart back or push her out completely. Mark is a man who prides himself in status. He has to "die" the most demeaning way, and in this case, his prestigious job as a spy is thrown back in his face by the man with the "pink socks"; his replacement at work. And Mark seems to welcome it with open arms. He is ready for his identity to "die" because it's become too painful.

Mark has over-exaggerated this bloody finale in his mind, but in reality he is simply deciding to move on from Anna. I believe Mark also sees Anna's behavior in a more dramatized way. So every time you see Anna have a breakdown, or appear to be completely violent, chaotic, and unreasonable, it is actually Mark's interpretation of reality. He's seeing Anna through this filter of anger and confusion. All of her reasons for leaving and wanting a divorce, and all of her explanations are just seen as violent outbursts, unfairly attacking him.

I don't believe the Anna we see is the true Anna. We do see glimpses, like when she is calmly in the room before the couple start arguing. Then Mark's over dramatization of her reaction to the fight is seen. I also believe her speech i.e. "you say I for me..." was the only true look at who Anna was as a troubled woman. She describes in heartbreaking detail how she struggles with understanding what she truly wants... marriage, commitment, and faith - and being a possession to Mark, or a life of excitement, chance, and most importantly an independent identity from her husband.

The doppelgängers, therefore, are Mark's and Anna's idealization of the perfect union, of a perfect partnership. For Mark, the double is the woman he believed Anna to be before they got married, and before the pressure of being a perfect wife and mother in an endless routine began to unravel her mind.

Anna struggles with identity, of desperately wanting to end the frustration and pain of indecision, almost to the point of wanting some person (or god, religion, or any force stronger than her) to tell her exactly what to want... and yet at the same time being fiercely afraid of making the wrong decision. However, I believe to her core, Anna desperately wants a man who knows all this about her and still wants her, instead of finding her indecision or her identity confusion 'vulgar.'

At the end, the real Anna and Mark 'die' (give up and give in), and their perfect other halves come together to try again. Except each "perfect" half is just the projection of what they think the other person wants. In reality, they will never be what the other person thinks they want, and their eventual attempts to seek happiness elsewhere will keep creating casualties. It's the most tragic love story because it happens all the time.

or like I said I could be wrong. I just saw the film before I posted this so I think i need to let the film settle and digest a bit. I will say I am pretty sure this is one of the most heartbreaking films I've ever seen.