Which mode is best to play in 8 Ball Pool that will give us more coins to get into exclusive matches?

Both modes are best while the 8 player tournament gives you exclusive rewards, the one on one matches provide you with the supply of coins that can be used to enter further exclusive events and matches but remember winning is the key!

How can I get huge awards and increase my rank?

To get huge awards and increase your rank in the game you need to be consistent. Practice as much as you can and play as much as you can in order to win the most matches that will take you up on the leaderboard.