You will normally find that most ready made food mixes will have all the nutrients they need and normally this would be enough for a healthy hen.
We give our hens layers mash rather than pellets has all the same ingredients but we were advised as it's that little bit more awkard for them to eat it takes them that little bit longer and thus less time to get bored and into mischief!!!!!
They also have any green leftovers (no meat) from our table and a hand full of wheat and corn which they adore in the afternoon.
One note during winter we tend to switch over to growers mash just to give them a boost in the colder months. It doesnt seem to effect their egg production any more than the darker days anyway, and if it did i wouldnt be too overly bothered as they could probably do with the break anyway
We put apple vinegar into their water every time it is refilled, though make sure your water container is plastic if you do this! It supposedly has several attributes including keeping down worm infestations. When we started using it, it certainly improved the look of the birds coats as well.
We use Verm-x for worming, gets bit of a bad press on here but was recommended by our very good local poultry center and friend who has kept chickens for decades. We havent had any noticable problems in the 5 years of use. Remember that like humans a small amount of worms are actually benefical to the chicken its just when it becomes a large infestation that problems occur. Like i said we use Verm-x because it works for us that doesnt mean it will for everone.
We have a seperate grit and oyster shell containers like yourself. Something we were told to do to when our hens were laying thin shelled/soft eggs was to improve their calcium intake. Along with the oyster shells we were advised to recyle our old egg shells, we put them in the oven at about 180% for 10 to 15 mins to dry the left over white/yolk , you dont want to give them a taste for fresh egg now do we!! and then crush up and add to their feed container, seemed to work a treat.