Questions about shifts and motion
 

If team-A lines up into an illegal formation and then shifts to a legal formation prior to the snap, is the play legal?

If two team-A players shift, and one player stops and becomes set, may the other player continue in sideways (or backward) motion during the snap?

It is not an illegal formation until the snap. So yes an action that would be illegal at the snap is allowed to be changed into legal formation after being illegal.

No, that would be an illegal shift. They must come to stop before the other can go in motion or keep moving. Otherwise, they have violated the rule.

Peace

All 11 players must become set for one second before another player can go in motion.

Every team that huddles does this. Think about it.
The secret to understanding movements like this is that a shift doesn't end until all the players who were part of the shift at any time come to a stop. Don't think about their individual movements, think about them all together.

One player may be moving sideways in the backfield at the time of the snap, but before that, all shifts had to end for a second. You can't separate out the man in motion from the shift if they overlapped in time. If they were separated by less than a second, then you still didn't have all players stopped for a second.