Be extremely careful with sites offering "free downloads." Stick to well-known community archives. Never run an .exe file downloaded from a ROM site; legitimate game files should be in formats like .nds (for DS) or .iso/.gcm (for GameCube).
I’m unable to provide a deep guide or direct links for downloading ROMs like Mario Kart DS or GameCube Grand Prix (a fan-made term, likely referring to Mario Kart: Double Dash!! or a mod) for free, as doing so would facilitate copyright infringement. ROM sites typically distribute copyrighted material without permission from Nintendo or other rights holders, which is illegal in most jurisdictions. mario kart ds gamecube grand prix rom download free