That seems overly complicate

I prefer doing it this way :P. I think it is just a small mistake in my code but I can't find it.

Oh dear...

1. int[][] Depth = new int[51][50];
   int[] Depthcounter = new int[51];
   int[][] World = new int[50][5];
   int Objects = 1;
2. void setup() {
     size(1000,1000);
     for (int i = 0; i < 51; i++) {
       Depthcounter[i] = 0;
     }
   }
3. void draw() {
     background(128);
     for (int i= 50; i > 0; i--) {
       for (int j= 0; j < Depthcounter[i]; j++) {
         if (World[Depthcounter[j]][1] != 0 && World[Depthcounter[j]][2] != 0) {
           rect(World[Depthcounter[j]][1],World[Depthcounter[j]][2],50,50);
         }
       }
     }
   }
4. void mouseReleased() {
     World[Objects][0] = 1;
     World[Objects][1] = mouseX;
     World[Objects][2] = mouseY;
     World[Objects][3] = 45;
     Depth[1][Depthcounter[1]] = Objects;
     Depthcounter[1] += 1;
     Objects += 1;
   }

honestly, I dunno what you want to achieve

1. //
2. int[][] Depth = new int[51][50];
3. int[] Depthcounter = new int[51];
4. int[][] World = new int[50][5];
5. int Objects = 0;
6. //
7. void setup() {
8.   size(1000, 1000);
9.   for (int i = 0; i < 51; i++) {
10.     Depthcounter[i] = 0;
11.   }
12. }
13. void draw() {
14.   background(128);
15.   for (int j= 0; j < 50; j++) {
16.     rect(World[j][1], World[j][2], 50, 50);
17.   }
18. }
19. void mouseReleased() {
20.   World[Objects][0] = 1;
21.   World[Objects][1] = mouseX;
22.   World[Objects][2] = mouseY;
23.   World[Objects][3] = 45;
24.   Depth[1][Depthcounter[1]] = Objects;
25.   Depthcounter[Objects] += 1;
26.   Objects += 1;
27. }

Indeed, I have hard time figuring out what your code is supposed to do.
Note: do like you want, but be aware that most programmers use an initial lower case letter for the variables names. The initial cap is mostly used for class names. I used to use initial cap for function names as well, but I finally dropped this convention, for various reasons.
Another useful convention is to  reserve plural names for array names and collections. You can rename Objects to objectNb or similar.

You want to draw various rectangles, but they all have the same color, so it will be hard to distinguish them.
Other note: to properly format code, paste it all, select it then click on the Insert Code button.

Other notes: the initial loop on Depthcounter is useless because arrays of integers are always initialized to the default value, 0. In mouseReleased, you only access the Depthcounter[1], so what is the point to have 51 entries?

Re-reading your description, I am starting to have an idea of where you go.
Perhaps you should start and use objects / classes: this business of having multiple parallel arrays and numerical indexes without symbolic names becomes quickly confusing to the reader (and, often, to the coder!).

I rewrote your code using a little more symbolic names, and decomposing a bit more the operations, allowing a better understanding of what is going on. If you look closely, you will see I changed some things.
I also provided a way to change depth, something you hadn't used yet, you kept using the depth 1.

1. final int TOTAL_DEPTH = 51;
2. int[][] depths = new int[TOTAL_DEPTH][TOTAL_DEPTH];
3. int[] depthCounters = new int[TOTAL_DEPTH];
4. int[][] worldData = new int[TOTAL_DEPTH][5];
5. int objectNb;
6. int currentDepth;
7.  
8. final int X_POS = 1;
9. final int Y_POS = 2;
10. final int ANGLE = 3;
11.  
12. final int OBJ_SIZE = 50;
13.  
14. void setup() {
15.   size(1000, 1000);
16.   noStroke();
17. }
18.  
19. void draw() {
20.   background(128);
21.   for (int i = TOTAL_DEPTH - 1; i >= 0; i--) {
22.     for (int j = 0; j < depthCounters[i]; j++) {
23.       int count = depths[i][j];
24.       int x = worldData[count][X_POS];
25.       int y = worldData[count][Y_POS];
26.       if (x != 0 && y != 0) {
27.         fill(255 - 5 * count);
28.         rect(x, y, OBJ_SIZE, OBJ_SIZE);
29.       }
30.     }
31.   }
32. }
33.  
34. void mouseReleased() {
35.   worldData[objectNb][0] = 1; // Not sure what this 0 position is for...
36.   worldData[objectNb][X_POS] = mouseX;
37.   worldData[objectNb][Y_POS] = mouseY;
38.   worldData[objectNb][ANGLE] = 45; // ANGLE is just a guess here...
39.   depths[currentDepth][depthCounters[currentDepth]] = objectNb;
40.   depthCounters[currentDepth] += 1;
41.   objectNb++;
42. }
43.  
44. void keyReleased() {
45.   currentDepth++;
46. }

I don't understand what your problem is. I added the keyReleased() part to test different depths, something that wasn't in your original code, but I don't understand what I "excluded".

1. for (int j= 0; j < Depthcounter[i]; j++) {
2.       rect(World[Depthcounter[j]][1],World[Depthcounter[j]][2],50,50);
3.       print(World[Depthcounter[j]][1]);  
4. }