Hi!

"How do I draw a transparent background?" is a common question on this forum.
The simple answer is: "You don't."

There is nothing behind the background to see, so there is no reason to have a transparent background!
The alpha value of the color sent to background() is ignored!

As for your other question, see imageMode().

Are you drawing something between the black background and the transparent black rectangle?
If not, then the only thing you'll see through the transparent black rectangle is the solid black background!

1. void setup(){
2.   size(300,300,P3D);
3. }
4. void draw(){
5.   // Make the background be black (or maybe greenish if the mouse is clicked).
6.   background(0,mousePressed?64:0,mousePressed?64:0); 
7.   // Draw something interesting.
8.   pushMatrix();
9.   lights();
10.   fill(128,0,64);
11.   noStroke();
12.   translate(width/2.0,height/2.0, -100);
13.   rotateY(map(mouseX,0,width,-HALF_PI,HALF_PI));
14.   rotateX(map(mouseY,0,height,-HALF_PI,HALF_PI));
15.   scale(100);
16.   box(1);
17.   popMatrix();
18.   // Draw a transparent black rectangle over the scene.
19.   fill( 0,0,0, map(mouseX, 0, width, 0,255) );
20.   rect(0,0, width/2.0, height );
21. }

have

1. // paint something here to make sure there's something to hide/show
2. fill(255, 0, 0);
3. rect(100, 100, width, height);
4. // now hide it
   
5. SliderOpacity = map(SliderData, 0, 1020, 0, 255);
6. fill(0, 0, 0, SliderOpacity);
7. rect(0, 0, width, height);

Thank you so much, why didn't I see that again. Works perfectly now!