Confused on when to use RMS current or voltage in calculations (regarding rectifiers)
why is the power absorbed by the DC source : P=Vo*Io


This is making an approximation that the current is approximately constant (or we're defining \$I_0\$ to be the time average of the current). The voltage is known to be constant because it's the voltage of an ideal DC source.


  power absorbed in the resistor is P = (Irms)^2 * R


The rms current is the square root of the mean of the squared current. 

Therefore \$I_{rms}^2\$ is the mean of the squared current. Since the instantaneous power consumed by the resistor is \$ i^2(t)R\$, the mean of the squared current is exactly what we need to get the mean power consumption.