I put a 2.1 tire on rim that usually uses 2.0. When I pedal the rim bends on the sides My rear wheel bends and my bike frame is getting beaten by my rim.

Does your bike have quick releases? Did you tighten them correctly.

Yes it has quick releases and I don't think I tighten it corectly. I don't know.

Can you expand on what is bending ? Or is it that the wider tyre now
rubs on the frame ?

The rim with the tire are bending together but when I stop pedaling the rim and the tire are almost in the center.
With the 2.00 tire everything is normal but only with the wider one(2.10) is bending.

Likely its always done that but now, with the wider tire, the
clearance is too small. How much gap between the frame and tire where
it rubs?. Also the bending you describe could be frame flex more than
wheel flex.

First, no before it was not moving when I pedal. With the new wider tire it has like a a half centimeter from the frame on the one side from the other it has 1 centimeter so I think maybe there is a problem with my tightening I am not really sure and even when I put it in the center where on the both sides it has a 0.7 gap, it bends again on the side and again it has half centimeter from the frame on the one side from the other it has 1 centimeter again.

Is there any bearing play i.e. can you move/wobble the rim sideways with the
bike suspended in the air?

Now I was testing to see if it wobble and it turns out that the axle is sideways  and on the other side is like this 
Any ideas what's wrong?
Judging by your last photo you have somehow unscrewed your cup&amp;cone bearings at least partly, making your bearings extremely loose.
Bearing play should be carefully adjusted. You usually need special, thin wrenches to adjust bearing play.
You might have lost some bearing balls in the meantime. While you are at it you should re-grease them. Probably best to visit a bike shop.