Yeah stay away from corn.
His diet should consist of lots of hay and he should be fine, otherwise you may need to look into natural grains like oats (but be careful)
As for exercises? You can just let him be. As long as he has enough room to run around he'll be happy. However if you do want to work with him, lunging on a large lungeline would work, or running with him next to you on lead around an open space. Just remember to wear gloves and try not to get kicked.