Your code is full of inconsistencies that I can't untangle it!  

Here's a link I've found explaining differences between field & local variables in Java:

Thanks for the reply's! I cleaned up the code a bit and took out the main but now i'm getting an error as such "The nested type MainGame cannot hide an enclosing type". Thanks for the help.

Use <CTRL> + T to auto-format your code. After that, it's easier to find each enclosing pair!

The code is full of syntax and worse - logical errors so I have taken the liberty of cleaning up the code otherwise you are not going to get anywhere fast. BTW try any keep your code tidy - use the Edit | Auto format menu option

Main code tab

1. Enemy[] enemy;
2. Player play;
3. int lives=3;
4. 
   
5. void setup(){
6.   size(1000, 1000);
7.   smooth();
8.   // Create enemies
9.   enemy = new Enemy[3];
10.   enemy[0]= new Enemy (700, 100 + random(-50,50), 1, 3);
11.   enemy[1]= new Enemy(700, 400 + random(-50,50), 1, 3);
12.   enemy[2]= new Enemy(700, 700 + random(-50,50), 1, 3);
13.   // Create player
14.   play = new Player( width/2, height/2, lives);
15. }
16. 
    
17. void draw(){
18.   background(100, 50, 100);
19.   drawplayer();
20.   drawenemy();
21.   if (lives==0) {
22.     println("GAME OVER");
23.     exit();
24.   }
25. }
26. 
    
27. void drawplayer(){
28.   play.moves(mouseX, mouseY);
29.   play.display();
30. }
31. 
    
32. void drawenemy(){
33.   for(int i = 0; i < enemy.length; i++){
34.     enemy[i].moves();
35.     enemy[i].display();
36.   }
37. }

Characters.pde

1. public class Characters{
2.   protected float x;
3.   protected float y;
4.   protected float xspeed;
5.   protected float yspeed;
6. 
   
7.   public Characters(float xpos, float ypos, float xspeedpos, float yspeedpos){
8.     x=xpos;
9.     y=ypos;
10.     xspeed=xspeedpos;
11.     yspeed=yspeedpos;
12.   }
13. 
    
14.   public float getX() {
15.     return x;
16.   }
17. 
    
18.   public void setX(float xpos) {
19.     x=xpos;
20.   }
21. 
    
22.   public float getY(){
23.     return y;
24.   }
25. 
    
26.   public void setY(float ypos){
27.     y=ypos;
28.   }
29. 
    
30.   public float getXspeed(){
31.     return xspeed;
32.   }
33. 
    
34.   public void setXspeed(float xspeedpos){
35.     xspeed=xspeedpos;
36.   }
37. 
    
38.   public float getYspeed(){
39.     return yspeed;
40.   }
41. 
    
42.   public void setYspeed(float yspeedpos){
43.     yspeed=yspeedpos;
44.   }
45. 
    
46.   public void display(){
47.     rect(x, y, 10, 10);
48.   }
49. 
    
50.   public void moves(){
51.     y =  y + yspeed;
52.     x = x + xspeed;
53.   }
54. }

Enemy.pde

1. public class Enemy extends Characters {
2. 
   
3.   public Enemy (float xpos, float ypos, float xspeed, float yspeed) {
4.     super(xpos, ypos, xspeed, yspeed);
5.   }
6. 
   
7.   public void display() {
8.     fill(200);
9.     rect(x, y, 200, 200);
10.     fill(100, 100, 200);
11.     rect(x+ 40, y + 40, 20, 10);
12.     rect(x+ 140, y + 40, 20, 10);
13.     fill(200);
14.     rect(x + 50, y + 140, 100, 10);
15.   }
16. 
    
17.   public void moves() {
18.     y =  y + yspeed;
19.     if (y + 200 > height || y < 0){
20.       yspeed = yspeed * -1;
21.     }
22.     x = x + xspeed;
23.     if (x + 200 > width || x < 0){
24.       xspeed = xspeed * -1;
25.     }
26.   }
27. }

Player.pde

1. public class Player extends Characters {
2.   protected int nlives;
3. 
   
4.   public Player (float xpos, float ypos, int lives) {
5.     super(xpos, ypos,0,0);
6.     nlives=lives;
7.   }
8. 
   
9.   public void moves(float xpos, float ypos){
10.     x=xpos;
11.     y=ypos;
12.   }
13. 
    
14.   public void display(){
15.     fill(255);
16.     ellipse(x, y, 50, 100);
17.     fill(20);
18.     ellipse(x - 10, y - 15, 10, 10);
19.     ellipse(x + 10, y - 15, 10, 10);
20.     ellipse(x, y + 20, 10, 30);
21.   }
22. }

Thank you both for your help. quarks, your code compiled and ran which was amazing. i'm just having one problem now regarding the "enemy" characters. i'm assuming this is because i don't know how to trace the enemy location and determine if a life is lost. the character (mouse position) is supposed to lose a life if it collides with an enemy. after it hits an enemy, the enemies are supposed to scatter back to original positions as to not lose all three lives at once. after it collides three times and loses all three lives the game will end. i've tried numerous things but i think i'm having problems. thanks again.