Well, I took my rear tire off so I can get my new tire mounted at the Suzuki dealer tomorrow. Do I need to remove the sprocket or anything before taking it in? I don't want to get charged extra for anything

Pretty stupid question, so feel free to move to the appropriate forum if it doesn't go in this one

No, suzi dealer know what to do.

The cush drive with the sprocket just sits there. Comes right off.
Leave the brake rotor on. My dealer likes to balance the wheel with the brake rotor on.
But dealer smart - dealer know what to do. Have dealer check bearings, so take cush with you. Better to replace bearings if any doubt about it, though they are probably OK unless the seals went bad.

My dealer advised me to leave the spacers, sprocket carrier, and cush drive (if easily removable) at home. On some bikes, the cush spacers fall out... On others (typically Suzuki) the drive spacers are difficult to remove, and can be left on the wheel. Reason to leave the spacers is that they are easily lost, and usually aren't kept in stock.

As addidasguy mentioned, don't unbolt the sprocket, simply remove the sprocket carrier. It pulls right out of the wheel.