It looks like due to too much fertilizer and resulted many leaves suddenly got rust. What should I do with those leaves got some rust ? Keep it there or remove them all ?
Will they drop off automatically later on or not ?

Are you sure its not fertilizer burn? Can you send a picture? If the tip of the leaf is the only part affected then I would just hold off on the fertilizer for a while.

That's not rust.. That's sunburn. I'm guessing the leaves were already formed when you moved it outside (as opposed to the buds and leaves forming AFTER it was moved outside)?

I have found that leaves formed in indirect sun or sun-through-window get sunburned very easily when moved outside. In fact here in Colorado at high altitude, no matter what I do in that situation the sun will completely destroy the leaves, even if I attempt a slow hardening off. It was hard for me to accept this because I thought figs were rockstars of hot, dry and sunny climate, but not as much at high altitude. Wherever you are, you are likely OK if you make your transition very slow. 

Keep the leaves on. They're not diseased or unhealthy -- just damaged around the perimeters.
I'd move the plant to be eased off of the sun just a little until it resumes new growth.

Hi EDoukas,

Thanks for your comments. What you said is correct that I move this Italian Honey from the garage to outside to enjoy more sun for 4 to 5 hours per day then move back to garage before 5 pm etc. I have been doing this in the last 20 days once we have sunny day.