Does anyone know about how elite sharing works when one leaves a legion? If I have a lock on someone else's shared elite and I leave, does the alert/lock stay with me?

And if I alert and then leave, does the alert stay with that legion, or can I re-alert in the new legion?

I know if you leave the legion, the NPC leaves with you.

Saying that, I also think you can not re-alert it. You would be the only person able to see it

If you have a lock on an elite and leave the legion, your still on that NPC and when its killed you get your award.

If you alert an elite, then leave the legion, the elite leaves with you. You can't re-alert an elite.

That is correct. Once alerted you cannot re-alert it. However... If you return to the legion you alerted it in before its timer expires, the members of that legion who were there at the time of the alert can still dig it up from their news feed but not the alert button on the battle tab.

you cannot re-alert a ship to a new legion, i had this exact problem with my first elite.

the legion you leave can still attack it, and anyone who joins a legion AFTER the alert can see it and attack it.

you can only alert it once

Wrong.