Do you get rested xp?
Is it stupid to level two characters at the same time (rotating each day) rather than get one to max lvl the auto lvl the other ??
I believe that happens after you get your first awakening quest. It should then apply to your alts. Now, does it retroactively apply to the alts, or alts made after your first character gets through the awakening quest? I don’t know.
Do you get rested xp when logged out?
Nah, you get extra rewards for doing the Chaos dungeons.