re: Question about brown dress shoes with charcoal sport coat

If it's a dark charcoal it may be odd with navy pants but navy-gray is fine and extremely common. If it's charcoal with some texture/variation it's probably fine. And gray+navy+brown shoes/belt is definitely done and the consensus is probably that this is far preferable to black pants and black shoes. In professional settings I rarely ever see black pants+black shoes (or black shoes at all).

Honestly the part that sounds the weakest to me is the shirt. If it's a standard light blue dress shirt - good. Solid colored shirts should be white or light blue unless you're some dandy who can get those pairings right. Especially with navy pants.