I recall the manual stating to do the left first, then the right, but you will probably have to go back and forth a few times. You can also gravity bleed some systems where you just open the bleed nipple and let the fluid slowly work its way down. I straddled the front wheel to do the left one so I could reach both the lever and the spanner, but then my system wasn't empty or filled with air, I was simply flushing the fluid with new.
As for leaking from the lid of the m/c, that probably depends on what's causing the leak. The rubber bellows thing should seal against the outer lip, so if it's just that then it's probably just a bit of corrosion that's built up that needs cleaning off the base of the m/c.
Another tip I brought from another bike we have is to turn the bars to change the angle of the m/c and also the calipers to dislodge air. You'll get it!