To answer your questions:
I recommend driving to the stadium. I'm not crazy for the public transportation in KC, and driving is not an issue here. It's very easy to get around town.
As for a baseball card shop, I suggest The Baseball Card Store at 9637 W 87th Street in Overland Park. 913-962-1924. Closed on Sunday and Monday, open at 12:30pm til 6pm. Call to verify hours though. They deal in 50's to current issues of cards. I'm sure you will find something there to your liking.
Be sure to stop by Rally House / Kansas Sampler for some Royals gear.
You need to have some BBQ while in town. Check out Kansas City Joe's, formerly known as Oklahoma Joe's.
KC also has some great Italian, and I recommend Garozzo's. Go to the one at 4th and Harrison. It's the original location and has a nice vibe. Make sure you are hungry as they serve large portions.
I can't help you with tickets.
The best sports radio station in the country is here in KC, 810am. Locally owned and they have a great history.
As mentioned, stop by the Negro Leagues Museum. You will not be disappointed.
I am happy to have arranged Chamber of Commerce weather for your stay in KC!!!!!!!