In Voyager, he’s shown to have pips. In fact, switching him over to Command mode shows a deliberate animation of pips showing up on hid collar.
The EMH is never shown with pips on Voyager. The "ECH" was shown with pips appearing on its first appearance, however:
spoiler
The entire ECH subroutine was created as the result of The Doctor's daydreaming, so the visualisation of a rank appearing out of thin air makes sense in that context.
The only other time the ECH mode was used in a genuine emergency (Season 7, Episodes 16/17), he did not have pips.
They do, but only in the front.
The only reason to use the button is that when you press it, it lowers the window slightly so that it clears the door trim when you open it (the windows are frameless).
Although, I don't see why that couldn't have been integrated into a single mechanism rather than having two separate controls for the same function.