2) Nothing you have posted indicates any advantage to the offense.
Geez, oldtimer, you are high maintenance.
You asked for a response on whether the center is offsides... and yes, technically he can line up offsides if he takes some weird positions where his helmet is beyond the ball.
But everything else is a question of how the refs call a game.. whether any advantage is gained by moving the ball.
The ball length acts as the neutral zone.
Only the center can be in the neutral zone.
If the center moves the ball forward, he is, in effect, advancing the position of the neutral zone.
If the D is allowed to line up where the ref called the LOS, even if the center advances the ball forward pre-snap.. which places the D in the neutral zone.. if the linesmen call that encroachment then an advantage was gained.
Id the D make no adjustment to the ball and the linesmen do not care that they are now lined up over the ball.. then no advantage is gained.
If the D adjusts to where the center moves the ball and line up on that ball.. then an advantage was gained.
What happens the most in real life, in actual practice, is that some of the D line up before the center moves the ball and some line up after. Some will line up where the flags tell them the LOS is and some will line up on the ball.. both before and after the center moves it.
Since this never seems to be called... SOME of the D are at a disadvantage.
It is a pretty clear case.
NOW.. if both teams' centers move the ball forward.. then it is a wash.