How do you find out how many coins you have collected?

Solution 1:

On 27 of August 2014 Nintendo released an update for Mario Kart which included this option:

• Drivers will now have the option to display the course map on the TV screen during races
• Users will be able to check out statistics such as their total number of coins accumulated, win-loss record from online play, and their most frequently selected character overall
• Users will be able to change options of others’ Mario Kart TV downloaded highlight reels, such as changing the focus to a new character or event
• The order of the menu after each race will be changed to “Next Race”, followed by “Watch Highlight Reel”
• The game will remember the most recent customised kart settings that were selected, even if the Wii U system is powered down
• Improvements to stability of connection in online play to enhance the user experience

Source: Nintendo itself

Solution 2:

You can't, I was wondering that too and there is no option anywhere. Not even on the Gamepad when posting to Miiverse.

All unlockables: http://www.ign.com/wikis/mario-kart-8/Unlockables