1. Limit screws aren't designed to move the derailleur directly. Once correctly set, they seldom require re-adjustment.
2. Park Tool is your friend. Their website includes easy-to-understand step-by-step instructions for most bicycle assembly, maintenance and tuneing jobs.
3. Whenever a front derailleur refuses to perform to satisfaction after being futzed with for awhile, my recommendation is to start over from the very beginning. Disconnect the shift cable from the derailleur. Now find the Park Tool instructions for installing a front derailleur and START FROM THE VERY BEGINNING with the position of the derailleur on the seat tube. Follow all of the steps in order because each step affects the subsequent steps.
Good luck!