Can Network Analyzer measure Impedance, Conductance, Susceptance or is there a device that does all?
Most analyzers are designed to analyze components or circuits in low power domain. Low power here means several 100W.

For example, it is not possible to measure the impedanz of a choke or transformer with huge (several kg) iron cores with these devices. These devices are not able to deliver sufficient current to exceed the remanence. The situation is similar for bigger capacitors. The devices are not providing more than 60V, so it is not possible to measure a 450V cap. In such cases it is necessary to apply a power source and measure the step-response.
It is recommended to start with an estimation about the expected values. This helps to design the setup for measurements. Have a look on the specification/ ratings of your analyzer.