1.) If you have a brake pulling, I'd pull both front brake drums and check to see if you have a leaking wheel cylinder or grease seal.
2.) As far as the brake adjusting, that is done by using a 'brake spoon' thru the slot on the back of the backing plate (it will have a small rubber plug inserted to keep dirt/water out).
3.) When you had the wheel/brake drum removed, you should have seen the brake adjuster with the 'star' wheel. The spoon is used to screw the adjuster outwards to expand the brake shoes towards the drum. Adjust it until the wheel cannot be rotated, then back it off until there is just a slight drag felt when rotating the wheel.
I would leave the self adjuster mechanism in place- its there for a reason.
Neil