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Set a background to the area out of camera limits (Viewport Rect) in Unity3D

I am talking about the Camera settings in Unity3D.
I'm trying to figure out if I can change (at least) the background color of the gray area in the screenshot. The limits of the camera are changed programmatically. The motivation lies in the fact that the playing area has to change dynamically based on whether a child or an adult is playing. The screen is huge around more than 83 inches. When rescaling the playing area, the area that is not drawn is gray and a bit ugly, I would like to know if you can define at least the color, or better still if possible with an image.
The screenshot you see is the screen capture in fullscreen mode, so it includes all the pixels.
After this brief explanation in words and images, let's go to the specifics of the technical details. This is how I resize the room design area:
public static void SetViewportCalibration()
{
var camera = Camera.main;
camera.pixelRect = new Rect(MinX, MinY, MaxX, MaxY);
}
Is it possible to set the color of that gray area outside the new Rect(MinX, MinY, MaxX, MaxY)?

There's two ways off the top of my head to accomplish this. Both ways use two Cameras.
The first way. Create a second Camera. The second Camera should have Depth LESS than the dynamic camera. This second, "Background" camera can then display anything you'd like, for example, a separate Skybox, a separate UI, other scene content, etc. etc.
The second way. Your dynamic camera is actually not resized dynamically. Instead, render your camera to a Target Texture. Use this texture in a material, and assign the material to a Quad mesh (most appropriate). This mesh can then be used in your scene like any other 3D object, which means not only can you position it, but scale it and even rotate it. The new camera that you added can have it's own Skybox, UI etc. etc.
I would opt for the second way. Partly personal preference, but also because it sounds like it might suit your situation better and be easier to implement. You can also implement many more effects for extra "wow".

Try to create another camera with no objects in its view and the following settings:
Clear Flags: Solid Color,
Background: Pick a color,
ViewPort Rect: X = 0, y = 0, w = 1, h = 1,
Depth: A smaller value than the other camera (Set the depth of this camera to 0 and the depth of the other camera to 1)
This camera will work as background of your screen.
I hope that I understood the question :)

Texture rendering issue when scaling with a matrix

I am working on a game (in XNA/MonoGame) in which I have large world consisting of many individual tiles with different textures. I store my world as a 2D array and to render it, I simply loop through every tile and draw it at the correct position.
Recently I implemented a zoom feature in my camera. My game's camera is made in the 'usual' XNA way where you have create a matrix based on position and scale and that pass that into your SpriteBatch.Begin() calls. My transform matrix is calculated as so:
Transform = Matrix.Identity *
Matrix.CreateTranslation(-(int)Position.X, -(int)Position.Y, 0) *
Matrix.CreateTranslation(Origin.X, Origin.Y, 0) *
Matrix.CreateScale(Scale);
The problem I am now facing is when I zoom in (by changing the camera's scale variable) some tile textures look odd at some zoom levels. Here are some pictures showing what I mean:
Here is a map at perfectly fine zoom level:
Here is a zoomed out (and cropped) view of the same map, notice how the sand texture is wierdly "upscaled":
I do not have much experience with graphics programming and really have no idea what this is caused by, but it makes the map look very janky.

How to make 3d viewport available within a square?

How to make 3D Viewport within that 3D viewport square

You can use the Normalized Viewport Rectangles' approach, achieved by editing the Viewport Rect of the Camera.
The Documentation explains an example of split screen for a two-player game. You can adapt the explanation having the game in a particular area, and the GUI in the other screen space.
Normalized Viewport Rectangles
Normalized Viewport Rectangle is specifically for defining a certain
portion of the screen that the current camera view will be drawn upon.
You can put a map view in the lower-right hand corner of the screen,
or a missile-tip view in the upper-left corner. With a bit of design
work, you can use Viewport Rectangle to create some unique behaviors.
It’s easy to create a two-player split screen effect using Normalized
Viewport Rectangle. After you have created your two cameras, change
both camera’s H values to be 0.5 then set player one’s Y value to 0.5,
and player two’s Y value to 0. This will make player one’s camera
display from halfway up the screen to the top, and player two’s camera
start at the bottom and stop halfway up the screen.

Position object on screen in different resolutions / aspect ratios (orthographic)

To be honest I am quite lost with world, screen and viewport coordinates in Unity.
My question is rather simple: in a 2d game how do I place an object in bottom left corner no matter what the resolution and screen aspect ratio is?

It is a little vague your description, but I think your talking about this:
Vector3 screenPos = new Vector3(x,y,z);
camera.ScreenToWorldPoint(screenPos);
As a side note, there are specific algorithms for 2D Unity, search for that also.
For Orthographic check this unity space which might help you:
http://answers.unity3d.com/questions/501893/calculating-2d-camera-bounds.html

I see no one ever followed up on this. Let's get some terms straight first:
Camera.main = the main camera that is looking at your game world
"game world" = the entire game map you've drawn
World Point = an absolute, unique position in the game world. Can be 2D or 3D (x,y,z)
Screen Point = a 2D x,y location of a pixel on the screen
So, when you want to place an object (i.e.transform its location) what you are really doing is placing it somewhere within the Game World. If the camera happens to be looking at that location in the World then it will appear on screen.
To figure out what parts of the World are currently on screen, you must convert a Screen Point to a World Point. So...assuming your object's size is 20x20, try this:
//Attach this script to the item you want "pinned" to the bottom, left corner of the screen
void Update() {
//fetch the rectangle for the whole screen
Rect viewportRect = Camera.main.pixelRect; //again, this has nothing to do with the World, just the 2D screen "size", basically
//now, let's pick out a point on the screen - bottom, left corner - but leave room for the size of our 20x20 object
Vector3 newPos = new Vector3(viewportRect.xMin + 20, Camera.main.pixelHeight - 20, 0);
//now calculate where we need to place this item in the World so that it appears in our Camera's view (and, thus, the screen)
this.transform.position = Camera.main.ScreenToWorldPoint(newPos);
}
I'm 98% certain this is all accurate info but if someone sees a mistake please point it out.

Tracking Rotating Sprite

I am messing about in XNA and have run into a problem. I have a 48 * 48 sprite that I can keep track of its location in the game world by the top left corner of the sprite.
I want to be able to rotate the square and still keep track of the same point. For instance if I rotate 90degrees clockwise and the orginal X position was 200 the new X position should be 200 + 48(the size of the width of the image). Its fine for 90 degrees I am able to work that out in my head but each one in between is the problem!
I know there is probably some kind of formula to work this out.
Any help would be great! Oh the square is rotating on its center.
I'm just using spriteBatch.Draw()
spriteBatch.Draw( animations[currentAnimation].Texture,
Camera.WorldToScreen(WorldRectangle),
animations[currentAnimation].FrameRectangle,
color, rotationScale , new Vector2((float)frameHeight/2, (float)frameWidth/2), effect, TileMap.characterDepth);

If you have to keep track of a moving rotating sprite you can't use the top left corner, but its centroid. You already draw your sprite using the centroid to rotate it.
The problem is that the second parameter of your Draw call is a Rectangle, you sholud use a Vector2 position, instead.

You're building your application on top of a 3D graphics library. 3D graphics libraries are very good at solving this kind of problem! Break it down into smaller operations and let the library do the work for you.
First: it's easiest to think about these kinds of questions when you're working in model space rather than world space. In other words: you don't need to worry about where the rotating point is in absolute terms, you only need to worry about where it is relative to the untransformed model (in this case, your sprite without any rotation or translation).
So where is that? Simple:
var pt = new Vector3(-frameWidth / 2f, -frameHeight / 2f, 0f);
Your point of origin is the center of your sprite, so the center of your sprite in model space is (0, 0). This means that the top left corner of your sprite is half the width of the sprite in the negative x direction, and half the height of the sprite along the negative y direction.
Now create an object that represents the desired transformation. You can do this by creating a rotation matrix using XNA's built-in methods:
var transformation = Matrix.CreateRotationZ(MathHelper.ToRadians(90f));
Now apply the transformation to your original point:
var transformedPt = Vector3.Transform(pt, transformation);
This is still in model space, remember, so to get world coordinates you'll need to transform it into world space:
var transformedWorldX = transformedPt.X + spritePosition.X;
var transformedWorldY = transformedPt.Y + spritePosition.Y;
And there you go.