It is my understanding that a lateral is a glorified and planned fumble. With that in mind, any lateral to any person is legal, regardless of position, number, credence, nationality, race, gender, etc.
Just think of how teams run hook and laterals, and they lateral to whomever is on their team. Regardless of the LOS, a lateral is still a lateral.
A forward lateral is totally different. Only those ruled eligible, can receive a forward lateral pass. It is my understanding that they share before the game, what plays may require a player whom can be generally viewed as "ineligible", can/will be used as an eligible receiver. They must notify the Officials prior to the snap, and the Official will notify the opposing team.
Let's just think of this differently. It may have been a designed play, but let's say Tommy is running the ball out of a shotgun, a lineman gets pushed back far behind Tommy, and Tommy decides (while being tackled) that this lineman has a better chance to score than himself, so he pitches it back to him. The lineman then runs the ball in for a TD. Same thing, only, designed.
As for advancing a fumble. I may be incorrect in this, but it is my understanding that in college, any side of the ball can advance a fumble at any point in the game. However, in the NFL, only the player that fumbled can advance a fumble in the 2 minute warning. I don't know if this rule changed, but I know that the officials indicate "no advanced fumbles" prior to snaps with what we see as a "false start" call. I think this may even be the case on a fourth down too. An offensive player can recover the fumble, but it is a dead ball, so the ball is down where the ball is recovered.