What is the rule both NFL and High school for a back motioning towards the line and then out wide? What has to be done or not done for him to be able to move towards the line? He just has to either set or move parallel to the line before the snap correct?

As long as he is not going forwards (towards the line) at the snap he is legal.

A man in motion must be moving parallel to or away from the LOS.

Anytime a back moves forward before the snap he must come to a complete stop for one full second before the snap.

So a back in a 2 back shotgun formation where he is at a depth of 5 yards, cannot motion towards the line either perpendicular or at an angle to a depth of a yard and a half and then out wide now moving parallel to the line unless he comes to a stop first?

You can only have one man in motion at the snap and that motion must be parallel to or away from the LOS. What is described is an illegal shift.

The situation you describe could occur before the snap only if the first back comes to a complete stop and there is no motion for a complete second. Technically, the first back is not in motion but is performing a shift.

No, you misunderstood. Only 1 back moves. He is motioning out wide to make a block on a screen. But I do not want him to motion out and remain at the 5 yard depth. I want him to get closer to the line. The other back never moves before the snap. So does the one back have to shift up towards the line, stop, and then go in motion wide? Or can it be one continous motion as long as he is moving parallel at the snap?

I'm pretty sure you asking for NF ruling but I'll answer for NCAA. First, all players must come to a complete stop for 1 second prior to the snap or any motions. One player who is a back may go in motion as long as he is not moving forward at the snap. He may move forward in a way that does not simulate the start of the play or that will be a false start. At the snap he cannot be moving forward. Also during his motion he must stay in the backfield because if he is on the LOS then he will be in illegal motion since only a back can be in motion. If you want the back to be out wide he should shift to the LOS, pause for 1 second, move out wide, pause for another second, and then snap the ball. Again this is only for NCAA and most likely NF and NFL are different.

NFHS: It's OK for the back to move forward before the snap, as long as he's not moving forward at the snap. There's no need for him to pause for one second, because he already established himself as a back by lining up in the backfield. It's not technically a "shift" because he doesn't take a new set position before the snap.

Players in motion who started "from any position not clearly behind the line" must either pause for one second in the backfield or be at least five yards behind the line at the snap.

NFHS rules on motion are the same as NCAA except for a player who is considered on the line. What Jason mentioned is legal.

As an aside, difference between NCAA and NFHS on motion is a lineman under NFHS rules who goes in motion directly from the line must be 5 yards from the line at the snap.