The dress code is listed on disney's website - hopefully someone will have a link. Basically it precludes hats for men, tanktops, swimwear, torn clothing and clothing with offensive language or graphics. Disney's definition of business casual is much more relaxed than the corporate world - khaki shorts, jeans, sneakers, plain tee, polo etc. are all appropriate, as are more formal/dressier clothing.
If it is just you and DH, looking for a quiet dinner, you may want to plan for later in the evening, after the fireworks are over, or request to be seated in the wine room (no fireworks view). While it is not as loud and boisterous as a character meal, the layout and open kitchen combined with the crowds around fireworks time make it a bit loud and no so intimate. That said, we generally dine here twice each stay.