Is the local manager similar to a marketing guy?
No. The Local Manager (and the Regional Manager, for that manner) simply has an ability that triggers during your Working 9-to-5 Phase. He doesn't "stay out" doing anything. He is in your structure or he isn't, like every other employee but the marketers.
when he goes back to my hand, that restaurant will stay on the board forever?
Does that mean I only need 1 local manager to open all my restaurants?
Yes---just one manager and three/four turns, depending on how you count it.
* Manager trained;
* Manager places COMING SOON;
* It opens, and manager places another COMING SOON, and you can probably even fire your manager to save cash if you don't need his Drive-Thru ability;
* It opens.