I am trying to develop a game for Android using pygame.
It would be a platformer. To move the main charachter, I would make the game to wait for mouse events (like pygame.MOUSEBUTTONDOWN).
In order to do that on mobile, I'd like to create a graphic representation of a joypad with arrow keys to be shown on the bottom left corner of the screen.
Now, when the user touches one of the arrows, a MOUSEBUTTONDOWN event should be triggered and the charachter should move accordingly.
My question is: since the "joypad" object is a mere draw, how can I link it to the event with pygame?
Is there a way to do so? Should I use the pixel coordinates of the arrow keys of the joypad or is there a better choice?
As far as I know this is not possible.
When handling input, mouse input and touch input are to be handled separately.
So to answer the 2 questions you listed at the end: 

As far as I know there is no way to implement this functionality.
You could use the pixel coordinates of the arrows. However you can use Rects for that and test if the place of mouse input/touch input is inside the arrow button Rect with the collidepoint method

You can achieve that as follows:
arrow_left.collidepoint(mouse_x, mouse_y)
I hope this answer helped you!
pygame - link an object to mouse event