I can help to answer some of your questions, since this week DS is just in the middle of skipping from K to 1st. Our school district is also very much against the skip, and I assume that child's school has to advocate for the skip. In our case, our school principal requested a meeting with all the teachers that know DS, to ask them, what they think. They also gave DS an end of the first grade test, with some additional proof of DS's capabilities. (His test scores SB5, and WIAT were also included). Then we, as parents signed on it, and the whole proposal went to District to be approved.
I must say that DS's pullout gifted teacher is the main engine behind all of this, and without her it would not happened. It seems that she really understand DS, and is just amazed what he can do.
I think that grade skip is a good idea in our case. DS was complaining how K is very easy. His K teacher started to assign him independent work, which took him out of the classroom flow. He was always watching the other children, what they were doing. It made him feel little bit as a outcast, even thought he enjoyed the challenging work.
I think this way he can be with more of his equals, and it takes him away from the K's training (which he does not need) and puts him more into the learning environment.
Even though he is still many years ahead even compared to the first graders, he will feel more comfortable in a slightly grown up environment. He will still need some extra challenge for example in math, reading and science, but with writing he should be right on the same level.
I will let you know more in the future, how it is working.