Even a man with the best aim still leaves splatter on the seat and environs when standing to widdle. It may not necessarily be blatantly obvious, but the mist is most definitely there, even if big nasty droplets are not. For this reason, and for the sake of simple, basic hygiene, I believe we should, therefore, follow the cultural example of Muslim men and sit to do wee-wees.
No matter what your gender, the lid should always be closed when flushing for both #1's and #2's. Reason? I've seen footage of a flush in close-up slow-mo, and it is one of the most scary things I've ever seen. You've seen those slow-mo horror pics of a sneeze, with zillions of tiny sneeze droplets projecting out from your nose, all the way to Calcutta? Well, same thing with the toilet flush. Microscopic spray from the bowl sprays up into the room, carrying with it tiny particles of whatever little treasure you just deposited in the bowl. If you don't put the lid down, you breathe in these particles. Put down the lid when flushing!
Oh, and all public urinals, worldwide, should be banned IMHO! They're so sexist. I mean, there aren't any urinals in women's toilets; even though woman are quite capable, anatomically, of using them; so why should men be subjected to such a degrading ritual?
