Neji did see Kidoumaru's eyes, it just wasn't drawn just like Hinata's eyes weren't drawn during their fight whereas he was describing them.
When Kishimoto draws a Byakugan vision, he doesn't draw all what a Hyuga sees : it's impossible.
When Neji looked at Shino, the manga shows the bugs because it was the current point, Neji is still able to see though Shino but it's not drawn because the panel would be illegible.
It's the same when Neji and Hinata looked at each others with the Byakugan, there wasn't any background at all, all the panel was grey.
That doesn't mean when they look at the inner coil they become unable to see around them, just that the important point was to show the inner coils system.
I didn't answer the other thing because it was retarded.
You asked, you were answered. You don't like the answer, so be it.