Elder tree's city bike (ssp)

Here is another example of mash bullhorn + pista steam. It doesn't look so bad.

Are we looking at the same picture? That setup looks horrible. Both aesthetically and ergonomically. Those bullhorns need to be level anyway, so it doesn't make sense to use a pista stem. Especially if you're going to use a spacer stack like in the picture above. Not to mention that saddle angle. I wouldn't take any cues from that bike.

I wouldn't use bullhorns anyway, but that's your personal choice. If you do, set it up like this:

Or with a 17 degree stem like @Netakure mentioned.

I also think you need to rethink your wheels. You're going to buy a wheelset without brake tracks to use in combination with a brake, then replace the hub because it doesn't allow a freewheel, and also replace the nipples with red nipples? Keep it simple. Buy a wheelset with brake tracks and a singlespeed/fixed hub. Forget the red nipples. You also want to use two brakes if you're going to make your bike singlespeed (a front brake isn't enough).