Misguided pixels issue

Im making a little pokemon like game. Im generating map with script. I got an 2d array with values, empty game object and depending on the value Im adding component Sprite Renderer with proper sprite. As you can see there are strange vertical lines they are the issue. If we take a closer look we can notice that sprites looks good but that vertical line looks to be a one pixel width part of the first from left sprite. What I mean in my MiniMiasto2 former sprite first “tile” on he left from pure green tile is a part of the orange road. It seems that first columns of pixels are from previous(first from the left) sprite. When Im verticaly moving my camera/hero the effect disapears! I have also noticed that changing the filter mode on imported sprite changes the scale of the effect. Point is giving better results than trilinear and bilinear.
Ive dealt with the problem by scaling my gameobject by 1.01, but I would like to know why all that is happening.

Here I got another problem. Even tho the quailty of the screen shot is terrible we can notice that 45 degrees lines of the trees doesnt look good. Ive noticed that one pixel of my sprite is something around 4 pixels of my monitor. Is it possible to make it 1:1 ratio always? The vision sight of the hero doesnt really matters in this game, so I dont mind if on different PCs volume of seen worlds changes, but I would really like 1 pixel of my spirte represent one pixel of any monitor. Is it achivable?

Well, first you should make sure you disabled mipmapping and anisotropic filtering since both are pointless and mipmapping is can cause such color bleeding. However due to antialiasing you might see the bleeding anyways. An atlas should have at least a 1 pixel border around each sprite.

If you want to use mipmapping (maybe you plan to zoom out) you should make your images based on power of two sizes. Mipmapping only works well with power of 2 since each mip level will cut the size in half. Atlas textures are generally bad for mipmapping because the lowest levels will result in a completely wrong color as all tiles will be mixed up.