I have a very fussy eater (4) Who won't eat anythng anywhere. He will eat gluten free bread, plain crisps, apples, cakes, biscuits, jam, honey, cheese spread under jam, buckwheat pancakes (with cheese hidden in them) dried fruit, chips, scarmabled egg, yoghurt- um and that's about it. What I do now is give him a snacky luck I know he will eat, and then at tea time unless its a pancake day (tuesdays mainly) he gets given a proper tea. if he doesn't eat it I give him a supper of bread and honey and a rusk after his bath. His bread has a lot of different seeds hidden in it, and I've got pretty good at hiding extra nutrients in his food. I also add an iron supplemet to his juice (usually he has one freshly squeezed orange a day- he won't eat oranges but he will drink the juice).
Offering him a main meal each day was how I got him eating scrambled egg and chips so it can work but very slowly.
If he's eating elsewhere I don't think you need to worry about nutrients etc, it's just whether or not you want to break the power struggle (but don't back down if you go down that path).
DS1 is very bad a trying new foods, one thing that seems to have helped recently is to get him to try a tiny tiny tiny crumb of something on a daily basis (often I give him something I know he'll like- eg honey)- he's very slowly getting better at trying new things.
OIf course the other problem I have is that ds2 is now copying ds1.