Two questions about the movie Leviathan 2014

Hello,
Just saw the movie on the cinema.

1. On the event where the friends go for a shooting picnic, and Lilia and Dmitri is alone, that small child runs to the other to say that Dmitri is choking Lilia. But later on it's told that they were actually having sex there. Also, after that incident both Lila and Dmitri got injuries on their faces. And Dmitri told Lilia that they are innocent until other is proven. What really happened there at the picnic?

2. The night Lilia goes out at night to commit suicide, how come it's later found out that her death is set up to be a murder charge againt Kolya later on? Did the mayor's men accidently passed by when they saw here that night, or ,were they spying over what happens in that house of Kolya?

Thanks in advance.

The child saw them kissing, cuddling, fondling and didn't know what that was, but it seemed like choking to him, especially since she was probably heavy breathing/gasping. Her husband raced to where they were and even fired his gun, so he either beat them or they got injured while trying to get away. It was basically his word against theirs, so there was no legal evidence one way or the other.

The suicide was called a murder after the mayor talked to the priest to make the last of their legal problems with Kolya go away. He was basically framed to be sent to prison so his land could be taken easier. The bureaucracy, legal system and the church all conspired against Kolya for daring to question their authority.

__________________
It's what you learn after you know it all that counts. - John Wooden
My IMDb page

"It was basically his word against theirs, so there was no legal evidence one way or the other.
"

Then why Lilia and Dmitri talked about proofs and so, if they were the ones who were attacked? It seemed like they were worry about THEIR guilt.

I want to take you back to the scene at the picnic, when Kolya told Lilia and her friend "what two pretty women doing there cooking" or something like that. Lilia's friend laughed in response, while Lilia was seemed unhappy and disturb. Why is that? Is that was because she was, at that moment of time, unhappy by the fact that she is Kolya's wife and not Dmitri's?
Also, a bit later Lilia is seen walk away. Kolya asks her where and she replys rudly. At this scene Dmitri is helping with the food and not going with her. It is assumed that he joined her later, right? (she must have been stood in a visible place, so Dmitri will notice her and join her to be alone).

About the suicide- it was Lilia's decision alone. So when did the mayor found out and how? Also, how did he managed to collect so many convicts and evidences against Kolya?

They were worried about their guilt about adultery, not violence. She was upset probably because she doesn't like all the secrecy she has to go through to try to share her feelings. The director went out of his way to provide only so much information, so I'm giving you my interpretation.

"They were worried about their guilt about adultery"
But I guess that there is a proof for that, as Kolya caught them having sex, didn't he?

What about the whole suicide? How come the mayor came involved in Lilia alone's decision, and how come he knew?

There's no way to sort it completely out. You can interpret several ways but it's left pretty open. We don't get to know very much about them. They don't even seem to know that much about each other. The only person with any knowledge of the truth, or who even has access to it, is the fat-**** mayor who ends up being the only main character who doesn't end the movie either dead or miserable. All of those big empty views really magnify how powerless they are. What I got out of it was that you can't demand conclusions and answers from things. "Can you pull in the Leviathan with a fishhook"? There are things beyond peoples control.