How to know the number of coins that I have collected

The Temple run series is like jetpack joyride, it is based on momentum. You collect speed over running and the most efficient way to lose it is to 'resurrect' by using gems or wings depending on which game you play.

Tripping, or collecting powerups, has nothing to do with your speed.

I was frustrated with the same issue. I believe that the lifetime coins challenges do not start counting until after the objective is activated (which could be a bug). You probably activated Gold Miner first, collected nearly 400k coins, and then completed a separate challenge that then activated Midas Touch. From that point all coins collected applied to both Midas Touch and Gold Miner, but because Gold Miner was open first, it has more progress. And, of course, the Midas Touch progress bar is going to fill half as fast as Gold Miner's.

I actually stopped playing after I noticed this. Even though they decreased the +2 Gem Powerup to level 9, it will just take too long to complete the lifetime challenges. If it had been counting my true lifetime progress, they would have been completed already.