but like that my code will not look the same accross multiple resolutions

Exactly. It depends on your code how it will look at different resolutions.

Using size(screen.width, screen.height) in 1.5.1. or size(screenWidth, screenHeight) in newer versions of Processing will make sure the sketch window fills the whole screen. Then in your code you should avoid hardcoded numbers based on 640x480, but instead use width and height as much as possible.

Is there any way to write code for one resolution (say, 640x480) and scale it up to any resolution?

This is not a great solution because of the pixelation. However it is possible to draw to a PGraphics or get() the screen and then display-resize the resulting image to fill the whole screen with image(yourGameCanvas, 0, 0, width, height);

The best solution is to code everything proportional to width and height variables.