Are there star ranks like in mario kart wii in this game?

Star Ranks are a classification on how skilled a player is on Mario Kart: Super Circuit, Mario Kart DS, Mario Kart Wii, Mario Kart 7, and Mario Kart 8. The player earns them for Grand Prix and Mission Mode. There are three variations of star ranks. There's 1-star rank, 2-star rank, and 3-star rank, 3-star being the hardest to earn. To get the 1-star rank, the player needs to get 36 points or higher (54 or higher in later games). To get the 2-star rank, the player needs to get 38 points or higher (57 or higher in later games). To get the 3-star rank, the player needs to get a maximum of 40 points (60 in later games). However, in Mario Kart DS and Mario Kart Wii, falling off a pit at a certain time may cancel the star ranks in a cup. As well as hitting walls or colliding with fixed objects, driving off-road (unless it’s with a boost) and staying in 9-12th place for too long. Using Items to avoid getting hit by other items add bonuses to your Star Rank, as well as using these items to hit other players. It would make a good challenge if there is not one already.

I don't think there is, but it would be a nice addition, and then there could be a ranking to see whose got the most stars.

There kinda is, because there are online points and classifications on your profile, as well as points for your vs wins, battle wins and number of posts on the forum.