How to get free Diamonds
You can get free Diamonds primarily by levelling up. Each time you do so, you will nab yourself 10, completely free.
How to get free Fuel
If you have run out of Fuel you can normally continue playing for one more event by watching an advert. This is frustrating, but is better than having to wait an extra 15 minutes for one more bar of Fuel.
How to get free Coins
You can get 3,000 Coins completely free, just by linking your Facebook account to the game. Once you've done this, you are also able to interact with your friends' games to get even more rewards, so it is worth doing if you're serious about the game.