What's the difference between Upgrade, Ascent and Increasing points?

Upgrade - this involves consumption of fragments and gold to increase tower level, these increases are permanentAscent - this involves consu...

In battle mode, why is it sometimes particularly fast and sometimes particularly slow?

In Battle mode, the speed is determined by the speed, at which the opponent kills off monsters

Why does the same boss sometimes have really high HP and sometimes really low HP?

The HP of the boss depends on the Basic HP + 50% HP of the remaining monsters on the battlefield