Cascode Amplifier: clarifications about output resistance and working point of transistors
Voltage Amplifier :

The gm of the structure is still the gm of the bottom transistor while the output impedance is much higher than a CS amplifier.This helps boost the small signal gain of the device, provided the Io in the picture is also implemented as cascode, otherwise the gain will be limited by the output impedance of the current source Io.
However cascoding comes at the expense of reduced voltage headroom at the output.

Transconductance Amplifier:

The output of interest is the small signal output current , the gm of the device is unchanged, however the current into the load will be a higher fraction of gm.vi  due to its increased output impedance, more of the gm.vi current will into the load.

Current Sources :

The idea here is that an ideal current source has infinite output impedance , that is the current it sinks or sources is independent of the voltage across it.

Now when you implement the Io in the above image as a cascode , any small change at the output voltage should not change the Io value as it will mess up the biasing of the circuitry. If Io was just one PMOS , any change at the output would have directly changed its Vds and hence the mirroring of the current Io from the reference. Cascoding helps in reducing the change in Vds by a factor of gm.ro which helps it mirror better and be better current source.

I have assumed that you know how Io in the figure will be implemented, if not please go  through slides of Allen Philip online.