Is this legal?

If the QB is UC and his helmet breaks the C's hip, Why isn't he considered on the LOS?

Because there's a specific exception for one player in position to be able to take a hand-to-hand snap between the snapper's legs.

Is the right guard in a position to take a hand to hand snap?

Not one that goes between the snapper's legs!  Nobody is, in that formation.  I mean, just look at them.

Here's the relevant part of 7-2-3: "Of the players of A who are not on their line at the snap only one may penetrate the vertical plane through the waistline of his nearest teammate who is on his line. He must have his hands in position to receive the ball if it is snapped between the snapper’s legs but he is not required to receive the snap."

By now the definition's probably been renumbered from the edition I'm using, but here's the wording in Rule 2 that makes that player a back: "A back is any A player who has no part of his body breaking the plane of an imaginary line drawn parallel to the line of scrimmage through the waist of the nearest teammate who is legally on the line, except for the player under the snapper, who is also considered a back."  Why the definition doesn't use the same language as the formation requirement, rather than just "under the snapper", is beyond me.

If you want to have your guard be a back, you can do it if his hands are in place like that.  In that case he's not on the line but is a back, so you'd better make sure you have no more than 3 other backs in the formation.

I believe the person who receives the snap cannot be on LOS.

Originally, yes, it was for safety.  7 on the line had been the common number to play with since 1880, when the total number a side was set at 11.  Walter Camp or some other commenter years later said that if they ever increased the number of players, the extras would undoubtedly be put on the line, because at that time (pre forward pass but also pre neutral zone and pre some of the other tactics I'll describe) it was seen as advantageous to the offense to do so, and defenses would need to follow.  The Eton field football game, which was the inspiration for 11 a side, uses 8 forwards and only 3 backs.

Because there was no neutral zone, originally the line players shoved against each other over that space before the ball was put in play.  Later in the 19th Century, teams first saw the advantages of starting their line charge on a snap count, instead of contesting the space that would later become the neutral zone.  Further, although teams most of the time would still play with 7 on the line, it was found advantageous for some of the O line to start in the backfield and get a running start to their interference.  Because of the increased danger, first a rule was made to require at least 6 on the line, and in 1906 (along with the introduction of the neutral zone and the forward pass) that was increased to 7, which was convenient because then they also had a basis to limit the number of eligible forward pass receivers.

Canadian football until 1966 required only a minimum of 5 on the line if no forward pass was thrown.  On plays with a forward pass, at least 7 on the line were required.  It was really only advantageous for protection against a blocked kick to have extra backs.

But if you're asking why the rule was made forbidding putting the ball into play by passing from one line player to another, that had nothing to do with safety.  When the snap was formalized, they wanted to make clear by rule when the ball would be in play.  The ball would be in play originally when it was moved by foot by the player entitled to do so.  However, previously the ball could not be handled "in scrimmage", so it had to leave the space between the forwards before it could be picked up.  At some point early in the 1880s that form of restriction was abolished, and in its place was put a requirement that the ball be kicked forwards or heeled backwards clearly out of scrimmage.  That is, the ball would no longer be live while in scrimmage except for the fraction of a second it took for it to leave that space.  From that point players of both sides were allowed to move their feet to an offside position -- ahead of the ball -- although theoretically players on offense were still restricted against interfering with play while offside.

I could tell you a lot more about the A11 and how it changed things, but I have to go speak at a clinic. 

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