I was playing my first game of the preseason as shaco and there was a katarina on the enemy team. I used my clone to get away but as she e'd my clone, it teleported to me (because I walked out of range) and she followed with my clone. Is that supposed to happen?
If she E's the exact milisecond your clone teleports back to your position, happens once in a blue moon =D
Yep. Targeted attacks will hit their target. It's why you cannot flash dodge the final banana. 
Lol.
Yes, all targeted abilities with travel time can do this, often with bizarre and hilarious effect. Only dashes that make you untargetable, like ekko R, block this.
Projectiles can also chase you across the map.
