What are Mechanics and Takedowns at the end of game statictics table of Heroes of the storm?

Takesdowns function similar to how lane minions give experience. As long as you're nearby or a part of the kill directly, you get the point for it. This should also carry across the mechanic that if you were a part of the kill in some way within the last 5 seconds, you will get the point as well. This would be healing, damaging, or things like Tyrande's Shadowstalk since it is buffing the ally that got the kill.

As for mechanics, these are directly related to the map mechanics themselves and has nothing to do with player encounters. The numbers, for the most part, aren't good indicators of how well you did mechanically, but more-so is the quantitative values earned for your team. You'd get these for things like picking up seeds for the Garden Terror, turning in doubloons (+1 per doubloon), gathering skulls in the mines, etc. If I remember right, merc camps don't reward any points towards this.