Mirror is relatively simple, you have two variants. You can do it by manipulating pixels or with scale() with -1 as a parameter.
By "inverted", I suppose you mean a complement of the colors. Use loadPixels(), iterate on the pixels, extract each color component, subtract it from 255, recompose the color and update the pixel. Use updatePixels() at the end. Perhaps a simple XOR of the color information (not the alpha one!) is enough...
If "inverted" means rotated by 180° (upside down), well, just do that...
I don't see what you mean by "image shot".

As he said, you can use scale()...
scale(-1, 1, 1) to flip...
scale(1, -1, 1) to invert.

For rotating, perhaps rotate() is useful...

I think efkolox in his 3rd point meant 90 degrees and 270 degrees ( = -90°)

that should be like

1. rotate(radians(90));

and

1. rotate(radians(-90));

Greetings!

In general, you have to use translate() to compensate the scale / rotate actions...

Example:

1. PImage niceImage;
2. 
   
3. void setup()
4. {
5.   size(1000, 800);
6.   smooth();
7.   noLoop();
8. 
   
9.   niceImage = loadImage("Globe.png");
10.   image(niceImage, 0, 0, niceImage.width, niceImage.height);
11. 
    
12.   drawInverted(niceImage);
13.   translate(niceImage.width, 0);
14.   drawReflected(niceImage);
15. }
16.  
17. void drawInverted(PImage img)
18. {
19.   pushMatrix();
20.   translate(img.width, img.height * 2);
21.   rotate(PI);
22.   image(img, 0, 0, img.width, img.height);
23.   popMatrix();
24. }
25.  
26. void drawReflected(PImage img)
27. {
28.   pushMatrix();
29.   translate(0, img.height);
30.   scale(1.00, -1.00);
31.   image(img, 0, -img.height, img.width, img.height);
32.   popMatrix();
33. }