With regard to your first question, the fourth value in fill sets the transparency. See example below.

1. void setup() {
2.   size(768,400,P2D);
3.   smooth();
4.   frameRate(30);
5. }
6. 
   
7. void draw() {
8.   background(255);
9.   gradient(frameCount % 255);
10. }
11. 
    
12. void gradient(int transparency) {
13.   noStroke();
14.   beginShape(QUADS);
15.   fill(188,190,192,transparency);
16.   vertex(0,0);
17.   vertex(width,0);
18.   fill(0,0,0,transparency);
19.   vertex(width,height);
20.   vertex(0,height);
21.   endShape();
22. }

With regard to pdf export. Check out the examples that come with Processing, the reference and the forum for info on different pdf export options. Try them and see if any of those options do what you want/need/expect.

thank you so much! this is exactly what i was looking for!:)

one more question please; how does it come that it needs the P2D mode and doesn't work without?

Amnon's code works for me with all of the render modes - though it looks drastically different in JAVA2D and has some artifact in P3D .. ??

really!? for me - if i just remove the P2D - the gradient doesn't show up ,the whole screen is slowely changing to black...?
thank you! and with P2D i can't export pdf...

The reference page for beginShape says (perhaps outdated):

"The P2D, P3D, and OPENGL renderer settings allow stroke() and fill() settings to be altered per-vertex, however the default JAVA2D renderer does not."

In general, there are differences between the renderers, that is why more options exist. Choose the renderer that best fits your needs in any particular situation. It's also possible to combine renderers through PGraphics + createGraphics.

Some research for different pdf export options was done in this thread.

In short, there are many different possible combinations / options. Just run some simple tests with different methods and compare the results. Then build on the one that best fits your needs.