Application of Bernoulli Energy Conservation In what cases does the static pressure decrease when the velocity increases in a flow.

And in what cases does the static pressure remain constant whilst the velocity and stagnation pressure increases?

Please answer with respect to Bernoulli's equation: Po1 = Ps1 + 0.5*rho*v1^2

For example in a closed circuit wind tunnel to what extent does the fan convert static pressure to dynamic pressure and to what extent does it just add energy by increasing the dynamic pressure.
Bernoulli's equation holds only if there is no energy source in the system. Since the fan adds energy, Bernoulli's does not apply across the fan; in the context of 1-D flow, pressure changes discontinuously across the fan.

Due to conservation of mass (no mass source for a simple fan), airspeed cannot change discontinuously across the fan interface. Therefore, right after the fan interface, both the static pressure and the total pressure have increased.

For more information, refer to this tutorial.