How often do you get flats, and what causes them?

I would not make generalizations about TPI (other than maybe suppleness) as there are a lot of other factors to consider).

Why do you need tread? Some say volume and tire pressure are all you need to determine traction, although I find tread pretty useful for wet condition (mud, slime, grass).

Best possible tire? Anything high end tire by compass, clement, continental, or Schwalbe could be considered the best, but no one tire does it all. need to choose and prioritize for weight, speed, durability, road speed, off road speed puncture protection, price, tread, etc...