Check in shouldn't take more than 5 minutes, F line is almost always empty.
You'll be fine leaving at 7:30am. Personally I would feel comfortable even leaving at 8/8:30am. But since it's your first time might as well get there early to enjoy the lounge etc.
Enjoy the flight!
The question will still be TSA security. Does EK has its own TSA check point or the EK F passengers have to get on the TSA line like the rest of the cattle? I used to fly CX F and they had their own TSA check point right behind the desk. I was on my way to the lounge within 15 min.