Delphi 7 - How to tell if object touches a color or another object

I'm writing 2d mini-games for another program I'm working on.

Problem is that I have very limited knowledge on coding that works with colliding objects.

For Example: how to test if 2 spheres collide like in Agar.io
or how the blocks from tetris detect that they touch each other,
or how Snake detects that the snake bit itself/food (without looking if the epicenters/coordinates of the middle of the objects are equal).

I'm using Delphi 7.

Solution

Collision testing is easy.
If you want to test if two circles collide check the distance between their two center points:

In a plane the distance between to points is calculated with the Pythagorean theorem sqrt((x2-x1)^2+(y2-y1)^2).

if (sqrt((x2-x1)^2+(y2-y1)^2)) > (Radius(Circle1)+Radius(Circle2)) then 
//x1,y1 = center point of circle1
//x2,y2 = center point of circle2
//or more efficiently:
a:= (x2-x1)^2+(y2-y1)^2
b:= (Radius(Circle1)+Radius(Circle2))^2;
if a > b then

If you want to check if two boxes collide there's a standard RTL routine for that.

if IntersectRect(Rect1,Rect2) then ....

As far as the snake goes, the thing that you're describing:

if the epicenters/coordinates of the middle of the objects are equal

Is exactly how it can be done, but a faster alternative is to use a discrete grid with integer coordinates and call a collision when two parts of the snake are on the same cell.

type
  // The grid is initially empty except for a border around the edges
  TBodyPart = (bpNone, bpBorder, bpTail, bpBody, bpHead);
  TSnakeGrid = array[0..20,0..20] of TBodyPart;

  TSnake = class(TObject)
  private
     SnakeLength: integer;
     Grid: TSnakeGrid;
     .... 
     function IsCollision: boolean;

 function TSnake.IsCollision: boolean;
 begin
   Result:= Grid[Head.x, Head,y] <> bpEmpty;
 end;

 procedure TSnake.MoveSnake(Direction: TDirection);
 begin
   //Move the head
   Grid[Head.x, Head.y]:= bpBody;
   Inc(SnakeLength);
   case Direction of
     north: Dec(Head.y);
     south:= Inc(Head.y);
     west:= Dec(Head.x);
     east: Inc(Head.x);
   end; {case}
   if Grid[Head.x, Head.y] <> bpEmpty then Grid[Head.x,Head,y]:= bpHead
   else GameOver;
 end;

Google for "collision detection delphi vcl" and you will find lots of code.