What happens when a flagship is destroyed? I assume that you no longer get the Admiral's abilities? But that doesn't really make sense with Motti...

If your flagship is destroyed you loose all benefits of the Admiral. In the case of Motti, all ships loose his bonus hull, sometimes resulting in indirectly killed ships.

Edit: Also, welcome to the forums!

Edit2: Because I'm bad at explaining stuff, I'll try to explain Motti better.

You have an VSD with Motti on it and an ISD with 12/14 damage cards. The VSD is destroyed, destroying Motti. The ISD now has 12/11 damage cards, and is destroyed as it's damage has exceeded its hull.

Except with Rieekan where his benefits last until the end of the current turn. In later turns you get nothing.

Speaking of Reekan: Does his ability mean that a destroyed ship can be saved by passing an engineering token or revealing an engineering dial?

Speaking of Reekan: Does his ability mean that a destroyed ship can be saved by passing an engineering token or revealing an engineering dial?

No.

Essentially, the way it works is:

"This Ship would normally be destroyed now. Instead of being Destroyed Now, it will be Destroyed at the End of the Status Phase....."

Nothing stops that ship from being "Destroyed"... Even if you repair it, it was still "Destroyed", and the Effect kicked in...